Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20274313 | C2 | semidirect |
| 4. #20272778 | C2 | semidirect |
| 5. #20272770 | C2 | semidirect |
| 6. #20272765 | C2 | semidirect |
| 131. C53 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276760 | 2 |
| #20274313 | 2 |
| D8×#88322 | 2 |
| #20272778 | 2 |
| #20272770 | 2 |
| #20272765 | 2 |
| C53×#2224 | 2 |
| #12422 | 53 |