Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20283305 | C2 | semidirect |
| 2. #20276431 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20272822 | C2 | semidirect |
| 17. C53×#469 | C4 | semidirect |
| 31. #13133151 | D4 | semidirect |
| 40. C2×D8×C53 | C2×C4 | semidirect |
| 52. #106×C53 | C2×C4 | semidirect |
| 168. #469 | Dic53 | semidirect |
| 176. C53 | #12999 | semidirect |
| 183. C2×D8 | C2×Dic53 | semidirect |
| 209. #106 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283305 | 2 |
| #20276431 | 2 |
| C2×#16810405 | 2 |
| #20272822 | 2 |
| C2×C53×#469 | 2 |
| #12999 | 53 |