Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 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. #135×Dic53 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20275601 | C2 | semidirect |
| 5. #20272829 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 11. #16811063 | C4 | semidirect |
| 13. #16811058 | C4 | semidirect |
| 34. C2×Dic212 | C2×C4 | semidirect |
| 36. C2×D424 | C2×C4 | semidirect |
| 50. #13133157 | C2×C4 | semidirect |
| 189. #2143 | D53 | semidirect |
| 220. C53 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #135×Dic53 | 2 |
| #20276452 | 2 |
| #20275601 | 2 |
| #20272829 | 2 |
| #20272796 | 2 |
| C53×#2143 | 2 |
| #13027 | 53 |