Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20274889 | C2 | semidirect |
| 5. #20272573 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 149. #1286 | D53 | semidirect |
| 170. C53 | #10631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275538 | 2 |
| #20274889 | 2 |
| #20273384 | 2 |
| #20273382 | 2 |
| #20272573 | 2 |
| #20272559 | 2 |
| C53×#1286 | 2 |
| #10631 | 53 |