Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 2. #20276503 | C2 | semidirect |
| 4. #20272821 | C2 | semidirect |
| 19. C53×#349 | C4 | semidirect |
| 48. M32×C53 | C2×C4 | semidirect |
| 161. #349 | Dic53 | semidirect |
| 163. C53 | #12923 | semidirect |
| 183. M32 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283305 | 2 |
| #20276503 | 2 |
| #20274748 | 2 |
| #20272821 | 2 |
| C2×C53×#349 | 2 |
| #12923 | 53 |