Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20276509 | C2 | semidirect |
| 3. C2×#16810453 | C2 | semidirect |
| 6. #20272831 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 19. #16810406 | C4 | semidirect |
| 139. #1382 | D53 | semidirect |
| 161. C53 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283323 | 2 |
| #20276509 | 2 |
| C2×#16810453 | 2 |
| C2×#16810406 | 2 |
| #20274766 | 2 |
| #20272831 | 2 |
| C53×#1382 | 2 |
| #12927 | 53 |