Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20290290 | C2 | semidirect |
| 4. #20290288 | C2 | semidirect |
| 5. #20289610 | C2 | semidirect |
| 6. #20289610 | C2 | semidirect |
| 227. C53 | #8864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291569 | 2 |
| #20290840 | 2 |
| #20290290 | 2 |
| #20290288 | 2 |
| #20289610 | 2 |
| #20273034 | 2 |
| #8864 | 53 |