Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #443×C71 | C2 |
| socle | C2×C71 | D42 |
| hypercenter | #443 | D71 |
| hypocenter | C71 | #3293 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986816 | C2 | semidirect |
| 2. #17986813 | C2 | semidirect |
| 3. #17986379 | C2 | semidirect |
| 4. #17986275 | C2 | semidirect |
| 5. #17986274 | C2 | semidirect |
| 6. #17986183 | C2 | semidirect |
| 7. #17986117 | C2 | semidirect |
| 8. #443×C71 | C2 | semidirect |
| 100. C71 | #3293 | semidirect |
| 108. #443 | D71 | semidirect |