Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20274937 | C2 | semidirect |
| 5. #20274934 | C2 | semidirect |
| 6. #20272843 | C2 | semidirect |
| 7. C53×#1395 | C2 | semidirect |
| 21. #16810421 | C4 | semidirect |
| 22. #16810419 | C4 | semidirect |
| 188. #1395 | D53 | semidirect |
| 216. C53 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283779 | 2 |
| #20276398 | 2 |
| #20275096 | 2 |
| #20274937 | 2 |
| #20274934 | 2 |
| #20272843 | 2 |
| C53×#1395 | 2 |
| #12975 | 53 |