Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15667948 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×C16×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13083558 | — | 2 | 2 | no | — |
| 4 | C2×C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 5 | C16×C89 | C4 | 1 | 2 | yes | — |
| 6 | C2×C4×C89 | D4 | 1 | 1 | yes | characteristic |
| 7 | C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | C8×C89 | Q8 | 1 | 1 | yes | characteristic |
| 9 | #10623494 | — | 4 | 2 | no | — |
| 10 | C22×C89 | Q16 | 1 | 1 | yes | characteristic |
| 11 | C4×C89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 12 | C4×C89 | D8 | 1 | 1 | yes | characteristic |
| 13 | C2×C89 | — | 2 | 1 | no | — |
| 14 | C2×C89 | #107 | 1 | 1 | yes | characteristic |
| 15 | C89 | #368 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | #368 | — | 89 | 1 | no | maximal, Sylow |
| 17 | C2×C16 | D89 | 1 | 1 | yes | characteristic |
| 18 | #108 | — | 89 | 2 | no | — |
| 19 | M16 | — | 178 | 2 | no | — |
| 20 | C2×C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 21 | C16 | Dic89 | 1 | 2 | yes | — |
| 22 | C2×C4 | D356 | 1 | 1 | yes | characteristic |
| 23 | C8 | — | 356 | 2 | no | — |
| 24 | C8 | Dic178 | 1 | 1 | yes | characteristic |
| 25 | C8 | C2×Dic89 | 1 | 1 | yes | characteristic |
| 26 | C22 | Dic356 | 1 | 1 | yes | characteristic |
| 27 | C4 | C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 28 | C4 | D712 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 2 | 1 | no | — |
| 30 | C2 | #15667946 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C89 | #368 | semidirect |