Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 480 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. #20283583 | C2 | semidirect |
| 5. #20272812 | C2 | semidirect |
| 6. #20272805 | C2 | semidirect |
| 7. C2×C53×#362 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 157. C2×#362 | D53 | semidirect |
| 185. C53 | #13018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133160 | 2 |
| #20283583 | 2 |
| #20276432 | 2 |
| #20275623 | 2 |
| #20272812 | 2 |
| #20272805 | 2 |
| C2×C53×#362 | 2 |
| #13018 | 53 |