Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 19. #16810450 | C4 | semidirect |
| 20. #16810450 | C4 | semidirect |
| 21. #16810449 | C4 | semidirect |
| 22. C53×#366 | C4 | semidirect |
| 145. #366 | #6157 | semidirect |
| 148. C53 | #13113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290823 | 2 |
| #20290519 | 2 |
| #20289776 | 2 |
| #20289775 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #20276496 | 2 |
| #13113 | 53 |