Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20277075 | C2 | semidirect |
| 3. #20275633 | C2 | semidirect |
| 4. #20273224 | C2 | semidirect |
| 5. #20273157 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 12. #16810914 | C4 | semidirect |
| 13. #16810819 | C4 | semidirect |
| 35. #13133217 | C2×C4 | semidirect |
| 36. #13133214 | C2×C4 | semidirect |
| 66. C4⋊C8×C53 | C2×C4 | semidirect |
| 156. D212 | #104 | semidirect |
| 196. #1285 | D53 | semidirect |
| 225. C53 | #9325 | semidirect |
| 254. C4⋊C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284807 | 2 |
| #20277075 | 2 |
| #20275633 | 2 |
| #20273224 | 2 |
| #20273157 | 2 |
| #20272607 | 2 |
| C53×#1285 | 2 |
| #9325 | 53 |