Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276509 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. #20276342 | C2 | semidirect |
| 6. #20274762 | C2 | semidirect |
| 7. C53×#1388 | C2 | semidirect |
| 164. #1388 | D53 | semidirect |
| 188. C53 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810894 | 2 |
| #20276509 | 2 |
| C2×#16810437 | 2 |
| C2×#16810435 | 2 |
| #20276342 | 2 |
| #20274762 | 2 |
| C53×#1388 | 2 |
| #13389 | 53 |