Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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. #20263954 | C2 | semidirect |
| 2. #20263945 | C2 | semidirect |
| 3. #20263935 | C2 | semidirect |
| 4. #20263934 | C2 | semidirect |
| 5. #20263934 | C2 | semidirect |
| 6. #20263933 | C2 | semidirect |
| 7. #20263920 | C2 | semidirect |
| 10. C4⋊C4×D199 | C2 | semidirect |
| 11. C2×C4⋊C4×C199 | C2 | semidirect |
| 38. C22⋊D199 | Q8 | semidirect |
| 74. C199 | #554 | semidirect |
| 86. C2×C4⋊C4 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263954 | 2 |
| #20263945 | 2 |
| #20263935 | 2 |
| #20263934 | 2 |
| #20263933 | 2 |
| #20263920 | 2 |
| C4×C22⋊D199 | 2 |
| C4⋊C4×D199 | 2 |
| C2×C4⋊C4×C199 | 2 |
| #554 | 199 |