Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×#13133287 | C2 | semidirect |
| 2. #20290274 | C2 | semidirect |
| 4. #20289601 | C2 | semidirect |
| 104. Q8×C53 | #108 | semidirect |
| 116. D212 | #108 | semidirect |
| 185. C53 | #8671 | semidirect |
| 265. Q8 | #13133287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133287 | 2 |
| #20290274 | 2 |
| #20290053 | 2 |
| #20289601 | 2 |
| C8×#11719949 | 2 |
| #8671 | 53 |