Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 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 | #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. #15668010 | C2 | semidirect |
| 2. #15668002 | C2 | semidirect |
| 3. #15668002 | C2 | semidirect |
| 4. #15667990 | C2 | semidirect |
| 5. #15667990 | C2 | semidirect |
| 6. #15667989 | C2 | semidirect |
| 7. #15667989 | C2 | semidirect |
| 8. #15667988 | C2 | semidirect |
| 9. #15667977 | C2 | semidirect |
| 13. C2×#13083553 | C2 | semidirect |
| 14. C4⋊C4×D89 | C2 | semidirect |
| 15. C22⋊Q8×C89 | C2 | semidirect |
| 61. C22⋊D89 | Q8 | semidirect |
| 101. C89 | #554 | semidirect |
| 111. C22⋊Q8 | D89 | semidirect |