Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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. C23×#88322 | C4 | semidirect |
| 7. C2×C22⋊#88322 | C4 | semidirect |
| 10. #16810347 | C4 | semidirect |
| 36. #99×C53 | C8 | semidirect |
| 163. C53 | #7204 | semidirect |
| 181. #99 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275008 | 2 |
| #20273036 | 2 |
| C4×#99×C53 | 2 |
| #7204 | 53 |