Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C22×C22⋊C4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C22⋊C4 | D71 |
| hypocenter | C71 | C22×#126 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556121 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic71 | C2 | semidirect |
| 3. C22×Dic71⋊C4 | C2 | semidirect |
| 4. C22×Dic71⋊C4 | C2 | semidirect |
| 7. C22×C4×Dic71 | C2 | semidirect |
| 13. #14556121 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic71 | C22 | semidirect |
| 15. C2×Dic71⋊C4 | C22 | semidirect |
| 16. C2×Dic71⋊C4 | C22 | semidirect |
| 19. C2×C4×Dic71 | C22 | semidirect |
| 32. C4⋊Dic71 | C23 | semidirect |
| 33. Dic71⋊C4 | C23 | semidirect |
| 34. Dic71⋊C4 | C23 | semidirect |
| 37. C4×Dic71 | C23 | semidirect |
| 73. C22×C71 | #126 | semidirect |
| 85. C2×C71 | C2×#126 | semidirect |
| 90. C71 | C22×#126 | semidirect |
| 163. C22 | #14556121 | direct (N × H) |
| 175. C2 | C2×#14556121 | direct (N × H) |