Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
752 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16810607 | C2 | semidirect |
| 3. C2×#16810419 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 5. C53×#1785 | C2 | semidirect |
| 49. #13133136 | D4 | semidirect |
| 251. #1785 | D53 | semidirect |
| 281. C53 | #13093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810607 | 2 |
| #20278330 | 2 |
| C2×#16810419 | 2 |
| #20272841 | 2 |
| C53×#1785 | 2 |
| #13093 | 53 |