Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
774 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 192 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. #20290647 | C2 | semidirect |
| 2. C42×#88324 | C2 | semidirect |
| 3. C2×D4⋊#88324 | C2 | semidirect |
| 23. C4×#88324 | D4 | semidirect |
| 40. #127×C53 | C8 | semidirect |
| 119. C4×C53 | D4⋊C8 | semidirect |
| 150. C53 | #9638 | semidirect |
| 157. #127 | #88324 | semidirect |
| 258. C4 | D4⋊#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290647 | 2 |
| C42×#88324 | 2 |
| C2×D4⋊#88324 | 2 |
| #127×Dic53 | 2 |
| #9638 | 53 |