Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 4. C2×C4⋊#88324 | C4 | semidirect |
| 8. C2×C4×#88324 | C4 | semidirect |
| 9. #16811468 | C4 | semidirect |
| 36. #13133132 | C8 | semidirect |
| 41. #99×C53 | C8 | semidirect |
| 185. C53 | #7205 | semidirect |
| 205. #99 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290836 | 2 |
| #20289951 | 2 |
| #99×Dic53 | 2 |
| #7205 | 53 |