Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 3. #20273489 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1301 | C2 | semidirect |
| 145. #1301 | D53 | semidirect |
| 167. C53 | #10637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274726 | 2 |
| #20274704 | 2 |
| #20273489 | 2 |
| #20273105 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| C53×#1301 | 2 |
| #10637 | 53 |