Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C137 | C2 |
| hypercenter | C4×D4 | D137 |
| hypocenter | C137 | #553 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984083 | C2 | semidirect |
| 2. #17984080 | C2 | semidirect |
| 3. #17984070 | C2 | semidirect |
| 4. #17984062 | C2 | semidirect |
| 5. #17984062 | C2 | semidirect |
| 6. #17984060 | C2 | semidirect |
| 7. C4×D548 | C2 | semidirect |
| 8. #17984048 | C2 | semidirect |
| 9. #17984047 | C2 | semidirect |
| 10. C2×C4⋊Dic137 | C2 | semidirect |
| 11. C4×D4×C137 | C2 | semidirect |
| 78. C137 | #553 | semidirect |
| 88. C4×D4 | D137 | semidirect |