Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
888 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 2. #20276143 | C2 | semidirect |
| 3. #20276138 | C2 | semidirect |
| 4. #20274905 | C2 | semidirect |
| 5. #20274811 | C2 | semidirect |
| 174. C53 | #27608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277307 | 2 |
| #20276143 | 2 |
| #20276138 | 2 |
| #20274905 | 2 |
| #20274811 | 2 |
| C53×#1780 | 2 |
| #27608 | 53 |