Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20263954 | C2 | semidirect |
| 2. #20263953 | C2 | semidirect |
| 3. #20263945 | C2 | semidirect |
| 7. C4×Dic398 | C2 | semidirect |
| 8. C4×Dic398 | C2 | semidirect |
| 11. C4×Q8×C199 | C2 | semidirect |
| 45. C4×D199 | Q8 | semidirect |
| 70. C199 | #533 | semidirect |
| 80. C4×Q8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263954 | 2 |
| #20263953 | 2 |
| #20263945 | 2 |
| #20263935 | 2 |
| #20263933 | 2 |
| #20263931 | 2 |
| C4×Dic398 | 2 |
| #20263912 | 2 |
| C42×D199 | 2 |
| C4×Q8×C199 | 2 |
| #533 | 199 |