Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
70 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11924591 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11924525 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×Q8×C37 | C4 | 1 | 1 | yes | characteristic |
| 4 | C2×D148 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×#64438 | — | 2 | 2 | no | — |
| 6 | #10596938 | — | 2 | 2 | no | — |
| 7 | C4×Dic37 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×D37 | — | 2 | 1 | no | — |
| 9 | Q8×C37 | — | 4 | 1 | no | — |
| 10 | C2×C4×C37 | — | 2 | 1 | no | — |
| 11 | C2×C4×C37 | C2×C4 | 1 | 1 | yes | characteristic |
| 12 | C2×Dic37 | D4 | 1 | 2 | yes | — |
| 13 | D148 | — | 4 | 1 | no | — |
| 14 | #64438 | — | 2 | 4 | no | — |
| 15 | C22×C37 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 16 | C2×D37 | — | 4 | 1 | no | — |
| 17 | C2×D37 | — | 4 | 2 | no | — |
| 18 | C4×C37 | — | 2 | 1 | no | — |
| 19 | C4×C37 | — | 4 | 1 | no | — |
| 20 | Dic37 | — | 2 | 2 | no | — |
| 21 | C2×C37 | #100 | 1 | 1 | yes | characteristic |
| 22 | C2×C37 | #104 | 1 | 2 | yes | — |
| 23 | D37 | — | 8 | 1 | no | — |
| 24 | #329 | — | 37 | 1 | no | maximal, Sylow |
| 25 | C37 | #329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 26 | #124 | — | 37 | 1 | no | — |
| 27 | #97 | — | 37 | 2 | no | — |
| 28 | C2×Q8 | #3866 | 1 | 1 | yes | characteristic |
| 29 | C2×D4 | — | 37 | 1 | no | — |
| 30 | C2×C8 | — | 74 | 2 | no | — |
| 31 | C22⋊C4 | — | 74 | 2 | no | — |
| 32 | C42 | — | 37 | 1 | no | — |
| 33 | C23 | — | 74 | 1 | no | — |
| 34 | Q8 | — | 4 | 1 | no | — |
| 35 | D4 | — | 148 | 1 | no | — |
| 36 | C2×C4 | — | 2 | 1 | no | — |
| 37 | C2×C4 | — | 37 | 2 | no | — |
| 38 | C2×C4 | C2×#3866 | 1 | 1 | yes | characteristic |
| 39 | C8 | — | 74 | 4 | no | — |
| 40 | C22 | — | 148 | 1 | no | — |
| 41 | C22 | — | 148 | 2 | no | — |
| 42 | C22 | C22⋊#3866 | 1 | 1 | yes | characteristic |
| 43 | C4 | — | 2 | 1 | no | — |
| 44 | C4 | — | 4 | 1 | no | — |
| 45 | C4 | — | 74 | 2 | no | — |
| 46 | C2 | — | 296 | 1 | no | — |
| 47 | C2 | #11924596 | 1 | 1 | yes | characteristic |
| 48 | C2 | #11924601 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924591 | C2 | semidirect |
| 25. C37 | #329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924591 | 2 |
| #11924525 | 2 |
| #329 | 37 |