Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273267 | C2 | semidirect |
| 5. #20273265 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1288 | C2 | semidirect |
| 11. #16810970 | C4 | semidirect |
| 12. #16810970 | C4 | semidirect |
| 29. #13133217 | C2×C4 | semidirect |
| 30. #13133217 | C2×C4 | semidirect |
| 58. C4×C8×C53 | C2×C4 | semidirect |
| 169. #1288 | D53 | semidirect |
| 192. C53 | #9425 | semidirect |
| 223. C4×C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285090 | 2 |
| #20277891 | 2 |
| #20273428 | 2 |
| #20273267 | 2 |
| #20273265 | 2 |
| #20272580 | 2 |
| C53×#1288 | 2 |
| #9425 | 53 |