Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #20283100 | C2 | semidirect |
| 3. #20275953 | C2 | semidirect |
| 4. #20275952 | C2 | semidirect |
| 7. #20275536 | C2 | semidirect |
| 8. #20274463 | C2 | semidirect |
| 9. C53×#1960 | C2 | semidirect |
| 173. #1960 | D53 | semidirect |
| 202. C53 | #30225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283100 | 2 |
| #20283073 | 2 |
| #20275953 | 2 |
| #20275952 | 2 |
| #20275539 | 2 |
| #20275538 | 2 |
| #20275536 | 2 |
| #20274463 | 2 |
| C53×#1960 | 2 |
| #30225 | 53 |