Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20276489 | C2 | semidirect |
| 2. #20276470 | C2 | semidirect |
| 6. #20275461 | C2 | semidirect |
| 7. C53×#1388 | C2 | semidirect |
| 143. #1388 | 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 |
|---|---|
| #20276489 | 2 |
| #20276470 | 2 |
| #20276452 | 2 |
| #20276442 | 2 |
| #20275601 | 2 |
| #20275461 | 2 |
| C53×#1388 | 2 |
| #13466 | 53 |