Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | C22⋊Q8×C89 | C2 |
| hypercenter | C22⋊Q8 | D89 |
| hypocenter | C89 | #548 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13083574 | C2 | semidirect |
| 2. C2×Q8×D89 | C2 | semidirect |
| 3. #15668001 | C2 | semidirect |
| 4. #15667998 | C2 | semidirect |
| 5. #15667990 | C2 | semidirect |
| 6. #15667987 | C2 | semidirect |
| 7. #15667985 | C2 | semidirect |
| 8. #15667977 | C2 | semidirect |
| 9. #15667974 | C2 | semidirect |
| 10. C4×C22⋊D89 | C2 | semidirect |
| 11. C22⋊Q8×C89 | C2 | semidirect |
| 58. Dic178 | D4 | semidirect |
| 68. C2×D89 | #41 | semidirect |
| 83. C89 | #548 | semidirect |
| 90. C22⋊Q8 | D89 | semidirect |