Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 4. #20275451 | C2 | semidirect |
| 5. #20272825 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C2×C53×#365 | C2 | semidirect |
| 18. #16810428 | C4 | semidirect |
| 19. #16810425 | C4 | semidirect |
| 92. Dic212 | C4⋊C4 | semidirect |
| 94. D424 | C4⋊C4 | semidirect |
| 151. C2×#365 | D53 | semidirect |
| 180. C53 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810744 | 2 |
| C2×#16810432 | 2 |
| #20276428 | 2 |
| #20275451 | 2 |
| #20272825 | 2 |
| #20272794 | 2 |
| C2×C53×#365 | 2 |
| #12955 | 53 |