Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
236 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276967 | C2 | semidirect |
| 4. #20272786 | C2 | semidirect |
| 5. #20272764 | C2 | semidirect |
| 6. #20272763 | C2 | semidirect |
| 77. D4×C53 | Q32 | semidirect |
| 133. C53 | #12431 | semidirect |
| 190. D4 | #13133163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276967 | 2 |
| D4×#11719908 | 2 |
| #20274080 | 2 |
| #20272786 | 2 |
| #20272764 | 2 |
| #20272763 | 2 |
| C53×#1669 | 2 |
| #12431 | 53 |