Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
14 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C16×C89 | C4 | 1 | 1 | yes | characteristic |
| 3 | C8×C89 | C8 | 1 | 1 | yes | characteristic |
| 4 | C4×C89 | C16 | 1 | 1 | yes | characteristic |
| 5 | C2×C89 | C32 | 1 | 1 | yes | characteristic |
| 6 | C89 | C64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | C64 | — | 89 | 1 | no | maximal, Sylow |
| 8 | C32 | D89 | 1 | 1 | yes | characteristic |
| 9 | C16 | Dic89 | 1 | 1 | yes | characteristic |
| 10 | C8 | #10623494 | 1 | 1 | yes | characteristic |
| 11 | C4 | #13083549 | 1 | 1 | yes | characteristic |
| 12 | C2 | #15667918 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D89 |
| commutator, hypocenter | C89 | C64 |
| Fitting | C32×C89 | C2 |
| socle | C2×C89 | C32 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C89 | C64 | semidirect |