Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×#117×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#117 | D71 |
| hypocenter | C71 | C2×#541 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986611 | C2 | direct (N × H) |
| 2. C2×#14556128 | C2 | semidirect |
| 4. C2×#14556120 | C2 | semidirect |
| 5. C2×#14556118 | C2 | semidirect |
| 7. C2×C4×Dic142 | C2 | semidirect |
| 10. #14556128 | C22 | semidirect |
| 12. #14556120 | C22 | semidirect |
| 13. #14556118 | C22 | semidirect |
| 15. C4×Dic142 | C22 | semidirect |
| 82. C2×C71 | #541 | semidirect |
| 86. C71 | C2×#541 | semidirect |
| 168. C2 | #17986611 | direct (N × H) |