Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274845 | C2 | semidirect |
| 3. #20273461 | C2 | semidirect |
| 6. #20272575 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 11. #16810700 | C4 | semidirect |
| 13. #16810688 | C4 | semidirect |
| 169. #1286 | D53 | semidirect |
| 195. C53 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283426 | 2 |
| #20274845 | 2 |
| #20273461 | 2 |
| #20273276 | 2 |
| #20273274 | 2 |
| #20272575 | 2 |
| C53×#1286 | 2 |
| #8678 | 53 |