Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16810443 | C2 | semidirect |
| 3. C2×#16810435 | C2 | semidirect |
| 4. #20276432 | C2 | semidirect |
| 5. #20276431 | C2 | semidirect |
| 6. #20274597 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 13. #16810998 | C4 | semidirect |
| 46. #13133151 | D4 | semidirect |
| 65. #108×C53 | D4 | semidirect |
| 170. C2×#361 | D53 | semidirect |
| 198. C53 | #13261 | semidirect |
| 232. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810998 | 2 |
| C2×#16810443 | 2 |
| C2×#16810435 | 2 |
| #20276432 | 2 |
| #20276431 | 2 |
| #20274597 | 2 |
| C2×C53×#361 | 2 |
| #13261 | 53 |