Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1212 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20283179 | C2 | semidirect |
| 3. #20276366 | C2 | semidirect |
| 4. #20276357 | C2 | semidirect |
| 5. C53×#2889 | C2 | semidirect |
| 6. C22×#11719949 | C4 | semidirect |
| 11. #16811187 | C4 | semidirect |
| 13. #16811130 | C4 | semidirect |
| 16. #16811101 | C4 | semidirect |
| 176. #2889 | D53 | semidirect |
| 205. C53 | #33351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288370 | 2 |
| #20283179 | 2 |
| #20276366 | 2 |
| #20276357 | 2 |
| C53×#2889 | 2 |
| #33351 | 53 |