Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1152 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 469 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×#125×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#125 | D71 |
| hypocenter | C71 | C2×#562 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986747 | C2 | direct (N × H) |
| 2. C2×#14556116 | C2 | semidirect |
| 3. C2×#14556113 | C2 | semidirect |
| 4. C2×#14556106 | C2 | semidirect |
| 5. C2×#14556103 | C2 | semidirect |
| 6. C2×#125×C71 | C2 | semidirect |
| 11. #14556116 | C22 | semidirect |
| 12. #14556113 | C22 | semidirect |
| 13. #14556106 | C22 | semidirect |
| 14. #14556103 | C22 | semidirect |
| 19. #125×C71 | C22 | semidirect |
| 71. C2×C71 | #562 | semidirect |
| 76. C71 | C2×#562 | semidirect |
| 78. C2×#125 | D71 | semidirect |
| 87. #125 | C2×D71 | semidirect |
| 148. C2 | #17986747 | direct (N × H) |