Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1194 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20283350 | C2 | semidirect |
| 3. #20275561 | C2 | semidirect |
| 4. #20275557 | C2 | semidirect |
| 6. #20274638 | C2 | semidirect |
| 196. C53 | #21802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811194 | 2 |
| #20283350 | 2 |
| #20275561 | 2 |
| #20275557 | 2 |
| #20274643 | 2 |
| #20274638 | 2 |
| C53×#1785 | 2 |
| #21802 | 53 |