Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20290605 | C2 | semidirect |
| 2. #20290569 | C2 | semidirect |
| 3. #20289533 | C2 | semidirect |
| 4. #20289531 | C2 | semidirect |
| 53. #121×C53 | C8 | semidirect |
| 229. C53 | #7599 | semidirect |
| 239. #121 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290605 | 2 |
| #20290569 | 2 |
| #20289533 | 2 |
| #20289531 | 2 |
| #121×Dic53 | 2 |
| #7599 | 53 |