Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 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 |
|---|---|---|
| 1. #20285463 | C2 | semidirect |
| 2. #20283967 | C2 | semidirect |
| 3. #20274627 | C2 | semidirect |
| 4. #20273076 | C2 | semidirect |
| 5. #20273075 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#3006 | C2 | semidirect |
| 249. #3006 | D53 | semidirect |
| 288. C53 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| #20283967 | 2 |
| #20274627 | 2 |
| #20273076 | 2 |
| #20273075 | 2 |
| #20272591 | 2 |
| C53×#3006 | 2 |
| #9974 | 53 |