Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. C4×#13133156 | C2 | semidirect |
| 3. #20273477 | C2 | semidirect |
| 4. #20272677 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. #20272675 | C2 | semidirect |
| 7. C53×#1331 | C2 | semidirect |
| 165. #1331 | D53 | semidirect |
| 191. C53 | #11675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285291 | 2 |
| C4×#13133156 | 2 |
| #20273477 | 2 |
| #20272677 | 2 |
| #20272676 | 2 |
| #20272675 | 2 |
| C53×#1331 | 2 |
| #11675 | 53 |