Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #554 |
| 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. #15668011 | C2 | semidirect |
| 2. #15668002 | C2 | semidirect |
| 3. #15667992 | C2 | semidirect |
| 4. #15667989 | C2 | semidirect |
| 5. #15667988 | C2 | semidirect |
| 6. Q8×Dic89 | C2 | semidirect |
| 9. C2×C4⋊Dic89 | C2 | semidirect |
| 10. C4⋊C4×D89 | C2 | semidirect |
| 11. C22⋊Q8×C89 | C2 | semidirect |
| 43. C22⋊D89 | Q8 | semidirect |
| 74. C89 | #554 | semidirect |
| 81. C22⋊Q8 | D89 | semidirect |