Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 13. #16811027 | C4 | semidirect |
| 14. #16811001 | C4 | semidirect |
| 19. C4×Dic212 | C4 | semidirect |
| 22. C4×Q16×C53 | C4 | semidirect |
| 157. C4×Q16 | #6157 | semidirect |
| 165. C53 | #11857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| #20290636 | 2 |
| #20289704 | 2 |
| #20289703 | 2 |
| #20285298 | 2 |
| #11857 | 53 |