Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20274707 | C2 | semidirect |
| 2. #20273033 | C2 | semidirect |
| 3. #20272721 | C2 | semidirect |
| 4. #20272718 | C2 | semidirect |
| 226. C53 | #11884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274707 | 2 |
| #20273033 | 2 |
| #20272721 | 2 |
| #20272718 | 2 |
| C53×#2543 | 2 |
| #11884 | 53 |