Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276387 | C2 | semidirect |
| 2. #20276384 | C2 | semidirect |
| 3. #20272886 | C2 | semidirect |
| 4. #20272878 | C2 | semidirect |
| 12. C53×#540 | C4 | semidirect |
| 14. C53×#496 | C4 | semidirect |
| 17. C53×#488 | C4 | semidirect |
| 22. C53×#433 | C4 | semidirect |
| 35. #127×C53 | C2×C4 | semidirect |
| 38. #125×C53 | C2×C4 | semidirect |
| 54. #97×C53 | C2×C4 | semidirect |
| 55. C4×C8×C53 | C2×C4 | semidirect |
| 165. #540 | Dic53 | semidirect |
| 167. #496 | Dic53 | semidirect |
| 170. #488 | Dic53 | semidirect |
| 175. #433 | Dic53 | semidirect |
| 182. C53 | #13609 | semidirect |
| 189. #127 | C2×Dic53 | semidirect |
| 192. #125 | C2×Dic53 | semidirect |
| 214. #97 | C2×Dic53 | semidirect |
| 215. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276387 | 2 |
| #20276384 | 2 |
| #20272886 | 2 |
| #20272878 | 2 |
| C53×#3220 | 2 |
| #13609 | 53 |