Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #20276311 | C2 | semidirect |
| 5. #20275501 | C2 | semidirect |
| 6. #20272825 | C2 | semidirect |
| 7. C53×#1381 | C2 | semidirect |
| 15. #16810435 | C4 | semidirect |
| 145. #1381 | D53 | semidirect |
| 168. C53 | #13144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810435 | 2 |
| C2×#16810425 | 2 |
| #20276311 | 2 |
| #20275623 | 2 |
| #20275501 | 2 |
| #20272825 | 2 |
| C53×#1381 | 2 |
| #13144 | 53 |