Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
826 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 144 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. #20289810 | C2 | semidirect |
| 3. #20289809 | C2 | semidirect |
| 7. #16811604 | C4 | semidirect |
| 11. C2×#13133174 | C4 | semidirect |
| 12. C2×C4⋊C4×D53 | C4 | semidirect |
| 13. #16810530 | C4 | semidirect |
| 18. C53×#391 | C4 | semidirect |
| 26. #13133276 | C2×C4 | semidirect |
| 199. #391 | #6157 | semidirect |
| 204. C53 | #12583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811604 | 2 |
| #20289810 | 2 |
| #20289809 | 2 |
| #20277306 | 2 |
| #12583 | 53 |