Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1010 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#16810360 | C2 | semidirect |
| 4. #20272593 | C2 | semidirect |
| 14. C2×C22⋊Q8×C53 | C4 | semidirect |
| 18. C53×#380 | C4 | semidirect |
| 195. C2×C22⋊Q8 | Dic53 | semidirect |
| 203. #380 | Dic53 | semidirect |
| 209. C53 | #9146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic53 | 2 |
| #20274625 | 2 |
| C2×#16810360 | 2 |
| #20272593 | 2 |
| C53×#2848 | 2 |
| #9146 | 53 |