Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20285942 | C2 | semidirect |
| 2. #20285097 | C2 | semidirect |
| 3. #20274049 | C2 | semidirect |
| 4. #20274043 | C2 | semidirect |
| 5. #20274038 | C2 | semidirect |
| 6. #20273353 | C2 | semidirect |
| 7. #20273322 | C2 | semidirect |
| 238. C53 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285942 | 2 |
| #20285097 | 2 |
| #20274049 | 2 |
| #20274043 | 2 |
| #20274038 | 2 |
| #20273353 | 2 |
| #20273322 | 2 |
| C53×#3531 | 2 |
| #19005 | 53 |