Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985861 |
| commutator | C23×C71 | C22×C4 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #344×C71 | C2 |
| socle | C2×C71 | #381 |
| hypercenter | #344 | D71 |
| hypocenter | C71 | #1829 |
| LCS | G ▷ C23×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #17985771 | C2 | semidirect |
| 5. #17985770 | C2 | semidirect |
| 6. #17985769 | C2 | semidirect |
| 7. #344×C71 | C2 | semidirect |
| 90. C71 | #1829 | semidirect |
| 97. #344 | D71 | semidirect |