Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
760 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #20275030 | C2 | semidirect |
| 3. C2×#16810358 | C2 | semidirect |
| 4. #20272979 | C2 | semidirect |
| 5. C53×#1280 | C2 | semidirect |
| 48. #13133124 | D4 | semidirect |
| 222. #1280 | D53 | semidirect |
| 249. C53 | #10402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280817 | 2 |
| #20275030 | 2 |
| C2×#16810358 | 2 |
| #20272979 | 2 |
| C53×#1280 | 2 |
| #10402 | 53 |