Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20272698 | C2 | semidirect |
| 5. #20272697 | C2 | semidirect |
| 6. #20272696 | C2 | semidirect |
| 7. C53×#1338 | C2 | semidirect |
| 146. #1338 | D53 | semidirect |
| 170. C53 | #11612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283646 | 2 |
| #20276469 | 2 |
| #346×D53 | 2 |
| #20272698 | 2 |
| #20272697 | 2 |
| #20272696 | 2 |
| C53×#1338 | 2 |
| #11612 | 53 |