Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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, socle | C23×C71 | C24 |
| Fitting | #399×C71 | C2 |
| hypercenter | #399 | D71 |
| hypocenter | C71 | #2842 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17985935 | C2 | semidirect |
| 2. #17985923 | C2 | semidirect |
| 3. #17985921 | C2 | semidirect |
| 5. #399×C71 | C2 | semidirect |
| 7. C2×C4⋊Dic71 | C22 | semidirect |
| 8. C2×Dic71⋊C4 | C22 | semidirect |
| 12. C71⋊#95 | C22 | semidirect |
| 13. C2×C4⋊C4×C71 | C22 | semidirect |
| 15. #95×C71 | C22 | semidirect |
| 67. C71 | #2842 | semidirect |
| 69. #399 | D71 | semidirect |
| 76. C2×C4⋊C4 | C2×D71 | semidirect |
| 82. #95 | C2×D71 | semidirect |