Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 9. #16811484 | C4 | semidirect |
| 13. C4×#11719908 | C4 | semidirect |
| 14. C4×C16×C53 | C4 | semidirect |
| 18. #13133285 | C8 | semidirect |
| 104. C4×C16 | #6157 | semidirect |
| 108. C53 | #7174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133285 | 2 |
| #20290263 | 2 |
| C4×#13133156 | 2 |
| #7174 | 53 |