Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D137 |
| commutator | C4×C137 | C24 |
| Frattini | C4 | C23×D137 |
| Fitting | 2−1+4×C137 | C2 |
| socle | C2×C137 | C22×D4 |
| hypercenter | 2−1+4 | D137 |
| hypocenter | C137 | #577 |
| LCS | G ▷ C4×C137 ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984134 | C2 | semidirect |
| 2. #17984119 | C2 | semidirect |
| 3. #17984113 | C2 | semidirect |
| 4. #17984108 | C2 | semidirect |
| 5. C2×#14555497 | C2 | semidirect |
| 6. #17984095 | C2 | semidirect |
| 7. 2−1+4×C137 | C2 | semidirect |
| 12. #14555500 | C22 | semidirect |
| 13. #14555498 | C22 | semidirect |
| 14. #14555497 | C22 | semidirect |
| 15. #14555497 | C22 | semidirect |
| 16. #14555495 | C22 | semidirect |
| 17. #14555494 | C22 | semidirect |
| 18. C2×#11764040 | C22 | semidirect |
| 21. #41×C137 | C22 | semidirect |
| 23. C2×Q8×C137 | C22 | semidirect |
| 53. C137 | #577 | semidirect |
| 55. 2−1+4 | D137 | semidirect |
| 66. #41 | C2×D137 | semidirect |
| 68. C2×Q8 | C2×D137 | semidirect |