Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
900 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 3. #20290254 | C2 | semidirect |
| 4. #20290230 | C2 | semidirect |
| 5. #20290224 | C2 | semidirect |
| 6. #20290220 | C2 | semidirect |
| 202. C53 | #17777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291647 | 2 |
| #20290254 | 2 |
| #20290230 | 2 |
| #20290224 | 2 |
| #20290220 | 2 |
| #20288528 | 2 |
| #17777 | 53 |