Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556103 |
| commutator | C2×C4×C71 | C22×C4 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #427×C71 | C2 |
| socle | C2×C71 | #390 |
| hypercenter | #427 | D71 |
| hypocenter | C71 | #1976 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986017 | C2 | semidirect |
| 3. #17985972 | C2 | semidirect |
| 4. #17985954 | C2 | semidirect |
| 5. #427×C71 | C2 | semidirect |
| 11. C2×Dic284 | C4 | semidirect |
| 12. C2×#11765854 | C4 | semidirect |
| 13. C2×D568 | C4 | semidirect |
| 97. C71 | #1976 | semidirect |
| 99. #427 | D71 | semidirect |