Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20274881 | C2 | semidirect |
| 3. #20274850 | C2 | semidirect |
| 5. #20272597 | C2 | semidirect |
| 6. #20272597 | C2 | semidirect |
| 22. #16810363 | C4 | semidirect |
| 44. #13133128 | C2×C4 | semidirect |
| 45. #13133128 | C2×C4 | semidirect |
| 229. C53 | #8911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277889 | 2 |
| #20274881 | 2 |
| #20274850 | 2 |
| C2×#16810363 | 2 |
| #20272597 | 2 |
| C53×#1959 | 2 |
| #8911 | 53 |