Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20291556 | C2 | semidirect |
| 2. #20290176 | C2 | semidirect |
| 3. #20290048 | C2 | semidirect |
| 4. #20289986 | C2 | semidirect |
| 5. #20289621 | C2 | semidirect |
| 6. #20289599 | C2 | semidirect |
| 240. C53 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291556 | 2 |
| #20290176 | 2 |
| #20290048 | 2 |
| #20289986 | 2 |
| #20289621 | 2 |
| #20289599 | 2 |
| #20284212 | 2 |
| #9349 | 53 |