Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20264001 | C2 | semidirect |
| 2. #20263986 | C2 | semidirect |
| 3. #20263980 | C2 | semidirect |
| 4. #20263975 | C2 | semidirect |
| 5. C2×#15691873 | C2 | semidirect |
| 6. #20263962 | C2 | semidirect |
| 7. 2−1+4×C199 | C2 | semidirect |
| 12. #15691876 | C22 | semidirect |
| 13. #15691874 | C22 | semidirect |
| 14. #15691873 | C22 | semidirect |
| 15. #15691873 | C22 | semidirect |
| 16. #15691871 | C22 | semidirect |
| 17. #15691870 | C22 | semidirect |
| 18. C2×C199⋊C8 | C22 | semidirect |
| 21. #41×C199 | C22 | semidirect |
| 23. C2×Q8×C199 | C22 | semidirect |
| 53. C199 | #577 | semidirect |
| 55. 2−1+4 | D199 | semidirect |
| 66. #41 | C2×D199 | semidirect |
| 68. C2×Q8 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20264001 | 2 |
| #20263986 | 2 |
| #20263980 | 2 |
| #20263975 | 2 |
| C2×#15691873 | 2 |
| #20263962 | 2 |
| 2−1+4×C199 | 2 |
| #577 | 199 |