Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
156 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 56 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. #20289737 | C2 | semidirect |
| 2. #20289628 | C2 | semidirect |
| 26. D8×C53 | C16 | semidirect |
| 80. C53 | #7070 | semidirect |
| 96. D8 | #11719910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289737 | 2 |
| #20289628 | 2 |
| D8×#88322 | 2 |
| #7070 | 53 |