Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20264003 | C2 | semidirect |
| 2. #20264002 | C2 | semidirect |
| 3. #20263988 | C2 | semidirect |
| 4. #20263987 | C2 | semidirect |
| 5. #20263984 | C2 | semidirect |
| 6. #20263976 | C2 | semidirect |
| 7. #20263975 | C2 | semidirect |
| 8. C2×#15691876 | C2 | semidirect |
| 9. Q16×D199 | C2 | semidirect |
| 10. #20263963 | C2 | semidirect |
| 11. #137×C199 | C2 | semidirect |
| 87. C199 | #578 | semidirect |
| 94. #137 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20264003 | 2 |
| #20264002 | 2 |
| #20263988 | 2 |
| #20263987 | 2 |
| #20263984 | 2 |
| #20263976 | 2 |
| #20263975 | 2 |
| C2×#15691876 | 2 |
| Q16×D199 | 2 |
| #20263963 | 2 |
| #137×C199 | 2 |
| #578 | 199 |