Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1606 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20277292 | C2 | semidirect |
| 3. #20275165 | C2 | semidirect |
| 4. #20274790 | C2 | semidirect |
| 5. #20274633 | C2 | semidirect |
| 6. C53×#1782 | C2 | semidirect |
| 9. C2×#13133213 | C4 | semidirect |
| 10. C2×#13133206 | C4 | semidirect |
| 11. C2×#13133191 | C4 | semidirect |
| 28. C22×C22⋊D53 | C2×C4 | semidirect |
| 36. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 41. C2×#11719921 | C2×C4 | semidirect |
| 43. C2×C4×Dic53 | C2×C4 | semidirect |
| 48. C22×Q8×C53 | C2×C4 | semidirect |
| 49. C22×D4×C53 | C2×C4 | semidirect |
| 51. C23×C4×C53 | C2×C4 | semidirect |
| 167. #1782 | D53 | semidirect |
| 190. C53 | #21750 | semidirect |
| 194. C22×Q8 | C4×D53 | semidirect |
| 200. C22×D4 | C4×D53 | semidirect |
| 203. C23×C4 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811187 | 2 |
| #20277292 | 2 |
| #20275165 | 2 |
| #20274790 | 2 |
| #20274633 | 2 |
| C53×#1782 | 2 |
| #21750 | 53 |