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 | #494×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #494 | D71 |
| hypocenter | C71 | D4×Q16 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #494 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×D71 | C2 | semidirect |
| 3. #17986237 | C2 | semidirect |
| 4. #17986206 | C2 | semidirect |
| 5. #17986153 | C2 | semidirect |
| 6. C4×Dic284 | C2 | semidirect |
| 8. #494×C71 | C2 | semidirect |
| 36. Dic284 | D4 | semidirect |
| 65. D284 | Q16 | semidirect |
| 78. C2×D71 | C2×Q16 | semidirect |
| 81. C4×C71 | C2×Q16 | semidirect |
| 92. C71 | D4×Q16 | semidirect |
| 95. #494 | D71 | semidirect |
| 176. C4 | Q16×D71 | semidirect |