Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20272727 | C2 | semidirect |
| 11. C22×Q16×C53 | C4 | semidirect |
| 16. C53×#467 | C4 | semidirect |
| 18. C2×#107×C53 | C4 | semidirect |
| 150. C22×Q16 | Dic53 | semidirect |
| 156. #467 | Dic53 | semidirect |
| 158. C2×#107 | Dic53 | semidirect |
| 165. C53 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276326 | 2 |
| #20274740 | 2 |
| #20272727 | 2 |
| C2×C53×#467 | 2 |
| #11889 | 53 |