Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #20272715 | C2 | semidirect |
| 11. C2×C4⋊Q8×C53 | C4 | semidirect |
| 14. C53×#397 | C4 | semidirect |
| 19. C4×C4⋊C4×C53 | C4 | semidirect |
| 171. C2×C4⋊Q8 | Dic53 | semidirect |
| 176. #397 | Dic53 | semidirect |
| 182. C4×C4⋊C4 | Dic53 | semidirect |
| 186. C53 | #11878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274703 | 2 |
| #20273033 | 2 |
| #20272715 | 2 |
| C53×#2547 | 2 |
| #11878 | 53 |