Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276400 | C2 | semidirect |
| 2. #20276380 | C2 | semidirect |
| 3. #20272872 | C2 | semidirect |
| 8. #16810420 | C22 | semidirect |
| 9. #16810418 | C22 | semidirect |
| 14. C2×#127×C53 | C4 | semidirect |
| 15. C53×#496 | C4 | semidirect |
| 19. C4×M16×C53 | C4 | semidirect |
| 164. C2×#127 | Dic53 | semidirect |
| 165. #496 | Dic53 | semidirect |
| 171. C4×M16 | Dic53 | semidirect |
| 176. C53 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276400 | 2 |
| #20276380 | 2 |
| #20272872 | 2 |
| C53×#3151 | 2 |
| #13579 | 53 |