Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
850 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20274832 | C2 | semidirect |
| 3. C2×#16810366 | C2 | semidirect |
| 4. C53×#1767 | C2 | semidirect |
| 38. C4⋊C8×C53 | D4 | semidirect |
| 123. #1767 | D53 | semidirect |
| 143. C53 | #9706 | semidirect |
| 165. C4⋊C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283110 | 2 |
| #20274832 | 2 |
| C2×#16810366 | 2 |
| C53×#1767 | 2 |
| #9706 | 53 |