Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1334 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 10. C2×#13133209 | C4 | semidirect |
| 11. C2×#13133208 | C4 | semidirect |
| 12. C2×#13133207 | C4 | semidirect |
| 17. C2×#125×C53 | C4 | semidirect |
| 139. C2×#125 | #6157 | semidirect |
| 148. C53 | #14664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811567 | 2 |
| #20289904 | 2 |
| #20289900 | 2 |
| C2×#125×D53 | 2 |
| #14664 | 53 |