Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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 | #462×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #462 | D71 |
| hypocenter | C71 | D4×Q16 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #462 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×D71 | C2 | semidirect |
| 4. #17986378 | C2 | semidirect |
| 5. #17986239 | C2 | semidirect |
| 6. #17986210 | C2 | semidirect |
| 7. #17986156 | C2 | semidirect |
| 8. #17986153 | C2 | semidirect |
| 9. C4×#11765855 | C2 | semidirect |
| 11. #462×C71 | C2 | semidirect |
| 57. #11765855 | D4 | semidirect |
| 97. D284 | Q16 | semidirect |
| 114. C2×D71 | C2×Q16 | semidirect |
| 119. C4×C71 | C2×Q16 | semidirect |
| 131. C71 | D4×Q16 | semidirect |
| 138. #462 | D71 | semidirect |
| 254. C4 | Q16×D71 | semidirect |