Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C2×#124×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#124 | D71 |
| hypocenter | C71 | #2326 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic71 | C2 | semidirect |
| 3. #17985906 | C2 | semidirect |
| 5. #17985892 | C2 | semidirect |
| 6. #17985874 | C2 | semidirect |
| 7. #17985869 | C2 | semidirect |
| 8. #17985845 | C2 | semidirect |
| 27. #124×C71 | C4 | semidirect |
| 49. C2×Q8×C71 | C2×C4 | semidirect |
| 56. C22⋊C4×C71 | C2×C4 | semidirect |
| 57. C42×C71 | C2×C4 | semidirect |
| 112. C71 | #2326 | semidirect |
| 125. #124 | Dic71 | semidirect |
| 145. C2×Q8 | C2×Dic71 | semidirect |
| 165. C22⋊C4 | C2×Dic71 | semidirect |
| 169. C42 | C2×Dic71 | semidirect |