Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20272703 | C2 | semidirect |
| 11. C22×Q16×C53 | C4 | semidirect |
| 14. C53×#470 | C4 | semidirect |
| 18. C53×#427 | C4 | semidirect |
| 148. C22×Q16 | Dic53 | semidirect |
| 152. #470 | Dic53 | semidirect |
| 157. #427 | Dic53 | semidirect |
| 163. C53 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276336 | 2 |
| #20274761 | 2 |
| #20272703 | 2 |
| C53×#3059 | 2 |
| #11869 | 53 |