Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 1. #20288525 | C2 | semidirect |
| 3. #20273756 | C2 | semidirect |
| 5. #20273226 | C2 | semidirect |
| 6. #20273059 | C2 | semidirect |
| 214. C53 | #18188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288525 | 2 |
| #20284814 | 2 |
| #20273756 | 2 |
| #20273654 | 2 |
| #20273226 | 2 |
| #20273059 | 2 |
| C53×#2398 | 2 |
| #18188 | 53 |