Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 116 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. C2×#16811509 | C2 | semidirect |
| 2. #20290262 | C2 | semidirect |
| 3. #20289672 | C2 | semidirect |
| 4. #20289670 | C2 | semidirect |
| 30. #13133239 | C8 | semidirect |
| 170. C53 | #11591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811509 | 2 |
| #20290262 | 2 |
| #20289672 | 2 |
| #20289670 | 2 |
| #20283486 | 2 |
| #11591 | 53 |