Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283795 | C2 | semidirect |
| 3. #20274708 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 196. #1286 | D53 | semidirect |
| 222. C53 | #9486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283795 | 2 |
| #20279625 | 2 |
| #20274708 | 2 |
| #20273141 | 2 |
| #20273139 | 2 |
| #20272573 | 2 |
| C53×#1286 | 2 |
| #9486 | 53 |