Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276487 | C2 | semidirect |
| 2. #20276471 | C2 | semidirect |
| 6. #20272826 | C2 | semidirect |
| 7. C53×#1945 | C2 | semidirect |
| 142. #1945 | D53 | semidirect |
| 164. C53 | #13466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276487 | 2 |
| #20276471 | 2 |
| #20276450 | 2 |
| #20276442 | 2 |
| #20275603 | 2 |
| #20272826 | 2 |
| C53×#1945 | 2 |
| #13466 | 53 |