Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1154 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16810419 | C2 | semidirect |
| 3. #20274643 | C2 | semidirect |
| 4. C53×#1785 | C2 | semidirect |
| 14. C2×#13133136 | C22 | semidirect |
| 19. C2×#101×C53 | C22 | semidirect |
| 202. #1785 | D53 | semidirect |
| 222. C2×#101 | C2×D53 | semidirect |
| 228. C53 | #12703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811187 | 2 |
| C2×#16810419 | 2 |
| #20274643 | 2 |
| C53×#1785 | 2 |
| #12703 | 53 |