Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 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 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | Q82×C71 | C2 |
| hypercenter | Q82 | D71 |
| hypocenter | C71 | Q8×#41 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986728 | C2 | semidirect |
| 2. #17986710 | C2 | semidirect |
| 3. Q8×D284 | C2 | semidirect |
| 4. #17986554 | C2 | semidirect |
| 6. C4×Q8×D71 | C2 | semidirect |
| 7. Q82×C71 | C2 | semidirect |
| 27. #11765866 | Q8 | direct (N × H) |
| 50. Q8×C71 | C2×Q8 | semidirect |
| 51. Q8×C71 | #41 | semidirect |
| 58. D284 | C2×Q8 | semidirect |
| 61. C4×D71 | C2×Q8 | semidirect |
| 78. C71 | Q8×#41 | semidirect |
| 79. Q82 | D71 | semidirect |
| 129. Q8 | Q8×D71 | semidirect |
| 130. Q8 | #11765866 | direct (N × H) |