Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20276451 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20272816 | C2 | semidirect |
| 16. C53×#470 | C4 | semidirect |
| 17. C53×#469 | C4 | semidirect |
| 34. #13133149 | D4 | semidirect |
| 39. C2×Q16×C53 | C2×C4 | semidirect |
| 41. C2×D8×C53 | C2×C4 | semidirect |
| 55. #106×C53 | C2×C4 | semidirect |
| 172. #470 | Dic53 | semidirect |
| 173. #469 | Dic53 | semidirect |
| 182. C53 | #13008 | semidirect |
| 187. C2×Q16 | C2×Dic53 | semidirect |
| 189. C2×D8 | C2×Dic53 | semidirect |
| 217. #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 |
| #20276451 | 2 |
| C2×#16810405 | 2 |
| #20272816 | 2 |
| C53×#3054 | 2 |
| #13008 | 53 |