Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 122 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. #20290432 | C2 | semidirect |
| 2. C4×#13133272 | C2 | semidirect |
| 4. #20289591 | C2 | semidirect |
| 12. #16811479 | C4 | semidirect |
| 29. #13133272 | C2×C4 | semidirect |
| 30. #13133272 | C2×C4 | semidirect |
| 207. C53 | #8226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290432 | 2 |
| C4×#13133272 | 2 |
| C2×#16811479 | 2 |
| #20289591 | 2 |
| #20277258 | 2 |
| #8226 | 53 |