Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20289865 | C2 | semidirect |
| 12. C2×Dic424 | C4 | semidirect |
| 16. Q32×D53 | C4 | semidirect |
| 19. C2×Q32×C53 | C4 | semidirect |
| 122. C2×Q32 | #6157 | semidirect |
| 130. C53 | #13618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| #20291066 | 2 |
| #20289865 | 2 |
| C2×Q32×D53 | 2 |
| #13618 | 53 |