Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 3. #20272890 | C2 | semidirect |
| 12. C2×#125×C53 | C4 | semidirect |
| 15. C53×#488 | C4 | semidirect |
| 19. C4×M16×C53 | C4 | semidirect |
| 137. C2×#125 | Dic53 | semidirect |
| 140. #488 | Dic53 | semidirect |
| 146. C4×M16 | Dic53 | semidirect |
| 151. C53 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276400 | 2 |
| #20276380 | 2 |
| #20272890 | 2 |
| C53×#3142 | 2 |
| #13604 | 53 |