Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D137 |
| commutator, socle | C22×C137 | C24 |
| Fitting | #123×C137 | C2 |
| hypercenter | #123 | D137 |
| hypocenter | C137 | #547 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555510 | C2 | semidirect |
| 2. C2×#14555509 | C2 | semidirect |
| 3. #17984087 | C2 | semidirect |
| 4. #17984073 | C2 | semidirect |
| 5. #17984072 | C2 | semidirect |
| 6. #17984070 | C2 | semidirect |
| 7. #17984066 | C2 | semidirect |
| 8. #17984065 | C2 | semidirect |
| 9. #17984061 | C2 | semidirect |
| 10. #17984060 | C2 | semidirect |
| 11. #17984048 | C2 | semidirect |
| 12. #17984048 | C2 | semidirect |
| 13. C2×#14555489 | C2 | semidirect |
| 14. C4⋊C4×D137 | C2 | semidirect |
| 15. #123×C137 | C2 | semidirect |
| 61. C22⋊D137 | D4 | semidirect |
| 107. Dic137 | #41 | semidirect |
| 115. C137 | #547 | semidirect |
| 123. #123 | D137 | semidirect |