Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20272704 | C2 | semidirect |
| 5. #20272703 | C2 | semidirect |
| 6. #20272702 | C2 | semidirect |
| 7. C53×#1340 | C2 | semidirect |
| 8. C2×Q16×D53 | C4 | semidirect |
| 12. #16810882 | C4 | semidirect |
| 14. #16810878 | C4 | semidirect |
| 18. #16810658 | C4 | semidirect |
| 179. #1340 | D53 | semidirect |
| 204. C53 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284368 | 2 |
| #20276334 | 2 |
| #20274760 | 2 |
| #20272704 | 2 |
| #20272703 | 2 |
| #20272702 | 2 |
| C53×#1340 | 2 |
| #11869 | 53 |