Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20275118 | C2 | semidirect |
| 4. #20272842 | C2 | semidirect |
| 5. C53×#1857 | C2 | semidirect |
| 50. #101×C53 | D4 | semidirect |
| 156. #1857 | D53 | semidirect |
| 178. C53 | #13426 | semidirect |
| 208. #101 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281741 | 2 |
| C2×#16810419 | 2 |
| #20275118 | 2 |
| #20272842 | 2 |
| C53×#1857 | 2 |
| #13426 | 53 |