Finite Group DatabasebetaFinite Group DatabasebetaOrder 23456.
62 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26044023 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | D733⋊C8 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #26044014 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19154469 | C22 | 1 | 1 | yes | characteristic |
| 5 | #19154469 | C22 | 1 | 3 | yes | — |
| 6 | D2932 | C4 | 1 | 3 | yes | — |
| 7 | C4×D733 | C22 | 1 | 3 | yes | — |
| 8 | Q8×C733 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×D733 | C2×C4 | 1 | 3 | yes | — |
| 10 | C4×C733 | C2×C4 | 1 | 3 | yes | — |
| 11 | Dic733 | C23 | 1 | 1 | yes | characteristic |
| 12 | C2×C733 | C22×C4 | 1 | 1 | yes | characteristic |
| 13 | D733 | — | 2 | 3 | no | — |
| 14 | C733 | #131 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | #131 | — | 733 | 1 | no | maximal, Sylow |
| 16 | #41 | — | 733 | 1 | no | — |
| 17 | M16 | — | 733 | 3 | no | — |
| 18 | C2×C8 | — | 733 | 3 | no | — |
| 19 | Q8 | #15668640 | 1 | 1 | yes | characteristic |
| 20 | D4 | — | 733 | 3 | no | — |
| 21 | C2×C4 | — | 733 | 3 | no | — |
| 22 | C8 | — | 733 | 1 | no | — |
| 23 | C8 | — | 733 | 3 | no | — |
| 24 | C22 | — | 733 | 3 | no | — |
| 25 | C4 | — | 733 | 1 | no | — |
| 26 | C4 | C2×#15668640 | 1 | 3 | yes | — |
| 27 | C2 | — | 1466 | 3 | no | — |
| 28 | C2 | C22×#15668640 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044023 | C2 | semidirect |
| 2. D733⋊C8 | C2 | semidirect |
| 14. C733 | #131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044023 | 2 |
| D733⋊C8 | 2 |
| #26044014 | 2 |
| #131 | 733 |