Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276942 | C2 | semidirect |
| 4. #20274332 | C2 | semidirect |
| 6. #20272631 | C2 | semidirect |
| 7. C53×#2241 | C2 | semidirect |
| 100. #2241 | D53 | semidirect |
| 125. C53 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276942 | 2 |
| #20276940 | 2 |
| #20276939 | 2 |
| #20274332 | 2 |
| #20274322 | 2 |
| #20272631 | 2 |
| C53×#2241 | 2 |
| #12512 | 53 |