Finite Group DatabasebetaFinite Group DatabasebetaOrder 6176.
44 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15690565 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C4×#11715871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #15690556 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#11715871 | — | 2 | 1 | no | — |
| 5 | #13095400 | — | 2 | 1 | no | — |
| 6 | D772 | — | 2 | 1 | no | — |
| 7 | D772 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C4×D193 | — | 2 | 1 | no | — |
| 9 | C4×D193 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×C193 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×D193 | — | 2 | 1 | no | — |
| 12 | C2×D193 | D4 | 1 | 1 | yes | characteristic |
| 13 | #11715871 | — | 2 | 2 | no | — |
| 14 | C4×C193 | — | 2 | 1 | no | — |
| 15 | C4×C193 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | Dic193 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×C193 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 18 | D193 | — | 2 | 1 | no | — |
| 19 | D193 | — | 4 | 1 | no | — |
| 20 | C193 | #104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | #104 | — | 193 | 1 | no | maximal, Sylow |
| 22 | #41 | — | 193 | 1 | no | — |
| 23 | M16 | — | 193 | 1 | no | — |
| 24 | C42 | — | 193 | 1 | no | — |
| 25 | Q8 | #11715871 | 1 | 1 | yes | characteristic, complemented |
| 26 | D4 | — | 386 | 1 | no | — |
| 27 | D4 | — | 193 | 1 | no | — |
| 28 | C2×C4 | — | 386 | 1 | no | — |
| 29 | C2×C4 | — | 386 | 1 | no | — |
| 30 | C2×C4 | — | 193 | 1 | no | — |
| 31 | C8 | — | 386 | 1 | no | — |
| 32 | C22 | — | 386 | 1 | no | — |
| 33 | C22 | — | 193 | 1 | no | — |
| 34 | C4 | — | 2 | 1 | no | — |
| 35 | C4 | — | 386 | 2 | no | — |
| 36 | C4 | — | 193 | 1 | no | — |
| 37 | C4 | C2×#11715871 | 1 | 1 | yes | characteristic |
| 38 | C2 | — | 772 | 1 | no | — |
| 39 | C2 | — | 386 | 1 | no | — |
| 40 | C2 | C22⋊#11715871 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690565 | C2 | semidirect |
| 2. C4×#11715871 | C2 | semidirect |
| 7. D772 | C4 | semidirect |
| 10. Q8×C193 | C4 | semidirect |
| 20. C193 | #104 | semidirect |
| 25. Q8 | #11715871 | semidirect |