Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 324 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. #20276514 | C2 | semidirect |
| 2. #20274846 | C2 | semidirect |
| 3. #20272727 | C2 | semidirect |
| 13. C53×#499 | C4 | semidirect |
| 14. C53×#495 | C4 | semidirect |
| 19. C4×Q16×C53 | C4 | semidirect |
| 21. C4×D8×C53 | C4 | semidirect |
| 148. #499 | Dic53 | semidirect |
| 149. #495 | Dic53 | semidirect |
| 154. C4×Q16 | Dic53 | semidirect |
| 156. C4×D8 | Dic53 | semidirect |
| 164. C53 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276514 | 2 |
| #20274846 | 2 |
| #20272727 | 2 |
| #20272724 | 2 |
| C53×#3168 | 2 |
| #11855 | 53 |