Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 68 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. #20290355 | C2 | semidirect |
| 3. #20289749 | C2 | semidirect |
| 4. #20289671 | C2 | semidirect |
| 6. #88324⋊C16 | C2 | semidirect |
| 85. #88324 | SD32 | semidirect |
| 128. C53 | #12070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290355 | 2 |
| D8×#88324 | 2 |
| #20289749 | 2 |
| #20289671 | 2 |
| #20289669 | 2 |
| #88324⋊C16 | 2 |
| SD32×Dic53 | 2 |
| #12070 | 53 |