Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 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. #20291079 | C2 | semidirect |
| 2. #20290636 | C2 | semidirect |
| 3. #20289703 | C2 | semidirect |
| 13. #16811024 | C4 | semidirect |
| 14. #16811008 | C4 | semidirect |
| 20. C4×D424 | C4 | semidirect |
| 22. C4×Q16×C53 | C4 | semidirect |
| 160. C4×Q16 | #6157 | semidirect |
| 170. C53 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20290636 | 2 |
| #20289703 | 2 |
| #20289702 | 2 |
| #20285288 | 2 |
| #11860 | 53 |