Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16810438 | C2 | semidirect |
| 4. #20276434 | C2 | semidirect |
| 6. #20272797 | C2 | semidirect |
| 7. C53×#1945 | C2 | semidirect |
| 160. #1945 | D53 | semidirect |
| 184. C53 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811007 | 2 |
| C2×#16810438 | 2 |
| C2×#16810435 | 2 |
| #20276434 | 2 |
| #20276430 | 2 |
| #20272797 | 2 |
| C53×#1945 | 2 |
| #13414 | 53 |