Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20291411 | C2 | semidirect |
| 2. #20290061 | C2 | semidirect |
| 3. #20290021 | C2 | semidirect |
| 4. #20290007 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289544 | C2 | semidirect |
| 256. C53 | #8996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291411 | 2 |
| #20290061 | 2 |
| #20290021 | 2 |
| #20290007 | 2 |
| #20289607 | 2 |
| #20289544 | 2 |
| #20284163 | 2 |
| #8996 | 53 |