Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277827 | C2 | semidirect |
| 2. #20273339 | C2 | semidirect |
| 3. #20273223 | C2 | semidirect |
| 4. #20272609 | C2 | semidirect |
| 19. C53×#497 | C4 | semidirect |
| 20. C53×#496 | C4 | semidirect |
| 48. C4⋊Q8×C53 | C2×C4 | semidirect |
| 49. #127×C53 | C2×C4 | semidirect |
| 58. #97×C53 | C2×C4 | semidirect |
| 180. #497 | Dic53 | semidirect |
| 181. #496 | Dic53 | semidirect |
| 193. C53 | #9441 | semidirect |
| 207. C4⋊Q8 | C2×Dic53 | semidirect |
| 208. #127 | C2×Dic53 | semidirect |
| 225. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277827 | 2 |
| #20273339 | 2 |
| #20273223 | 2 |
| #20272609 | 2 |
| C53×#3153 | 2 |
| #9441 | 53 |