Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20289881 | C2 | semidirect |
| 4. #20289880 | C2 | semidirect |
| 13. #16810456 | C4 | semidirect |
| 14. #16810456 | C4 | semidirect |
| 17. C2×#13133123 | C4 | semidirect |
| 18. C2×C32×C53 | C4 | semidirect |
| 93. C2×C32 | #6157 | semidirect |
| 98. C53 | #13638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| #20291066 | 2 |
| #20289881 | 2 |
| #20289880 | 2 |
| C2×#16810456 | 2 |
| #13638 | 53 |