Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
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. #20263372 | C2 | semidirect |
| 2. #20263357 | C2 | semidirect |
| 3. #20263351 | C2 | semidirect |
| 4. #20263346 | C2 | semidirect |
| 5. C2×#15691345 | C2 | semidirect |
| 6. #20263333 | C2 | semidirect |
| 7. 2−1+4×C197 | C2 | semidirect |
| 12. #15691348 | C22 | semidirect |
| 13. #15691346 | C22 | semidirect |
| 14. #15691345 | C22 | semidirect |
| 15. #15691345 | C22 | semidirect |
| 16. #15691343 | C22 | semidirect |
| 17. #15691342 | C22 | semidirect |
| 18. C2×#13096802 | C22 | semidirect |
| 21. #41×C197 | C22 | semidirect |
| 23. C2×Q8×C197 | C22 | semidirect |
| 53. C197 | #577 | semidirect |
| 55. 2−1+4 | D197 | semidirect |
| 66. #41 | C2×D197 | semidirect |
| 68. C2×Q8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263372 | 2 |
| #20263357 | 2 |
| #20263351 | 2 |
| #20263346 | 2 |
| C2×#15691345 | 2 |
| #20263333 | 2 |
| 2−1+4×C197 | 2 |
| #577 | 197 |