Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20274852 | C2 | semidirect |
| 3. #20273170 | C2 | semidirect |
| 6. C2×C8×#88322 | C2 | semidirect |
| 7. C53×#1493 | C2 | semidirect |
| 156. #1493 | D53 | semidirect |
| 184. C53 | #9857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285040 | 2 |
| #20274852 | 2 |
| #20273170 | 2 |
| #20273167 | 2 |
| #20273165 | 2 |
| C2×C8×#88322 | 2 |
| C53×#1493 | 2 |
| #9857 | 53 |