Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20279934 | C2 | semidirect |
| 5. #20272595 | C2 | semidirect |
| 6. #20272583 | C2 | semidirect |
| 7. C53×#1282 | C2 | semidirect |
| 219. #1282 | D53 | semidirect |
| 249. C53 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279934 | 2 |
| #20275551 | 2 |
| #20273284 | 2 |
| C2×#16810358 | 2 |
| #20272595 | 2 |
| #20272583 | 2 |
| C53×#1282 | 2 |
| #10376 | 53 |