Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #477×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #477 | D71 |
| hypocenter | C71 | #3079 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #477 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×D71 | C2 | semidirect |
| 3. #17986294 | C2 | semidirect |
| 4. #17986290 | C2 | semidirect |
| 5. #17986286 | C2 | semidirect |
| 6. #17986282 | C2 | semidirect |
| 7. #17986278 | C2 | semidirect |
| 8. #17986040 | C2 | semidirect |
| 9. #17986021 | C2 | semidirect |
| 11. #477×C71 | C2 | semidirect |
| 44. #11765866 | Q8 | semidirect |
| 86. Q8×C71 | C2×Q8 | semidirect |
| 100. D284 | C2×Q8 | semidirect |
| 138. C71 | #3079 | semidirect |
| 142. #477 | D71 | semidirect |
| 226. Q8 | Q8×D71 | semidirect |