Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290916 | C2 | semidirect |
| 2. #20290263 | C2 | semidirect |
| 3. #20289676 | C2 | semidirect |
| 4. #20289673 | C2 | semidirect |
| 30. #13133236 | C8 | semidirect |
| 170. C53 | #11597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290916 | 2 |
| #20290263 | 2 |
| #20289676 | 2 |
| #20289673 | 2 |
| C4×#13133236 | 2 |
| #11597 | 53 |