Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20291360 | C2 | semidirect |
| 2. #20290062 | C2 | semidirect |
| 3. #20290022 | C2 | semidirect |
| 4. #20290007 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289544 | C2 | semidirect |
| 260. C53 | #8995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291360 | 2 |
| #20290062 | 2 |
| #20290022 | 2 |
| #20290007 | 2 |
| #20289607 | 2 |
| #20289544 | 2 |
| #20284171 | 2 |
| #8995 | 53 |