Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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. #20283344 | C2 | semidirect |
| 3. #20275553 | C2 | semidirect |
| 4. #20274636 | C2 | semidirect |
| 5. #20274635 | C2 | semidirect |
| 6. C53×#1783 | C2 | semidirect |
| 16. #16810646 | C22 | semidirect |
| 17. C2×#13133134 | C22 | semidirect |
| 18. C2×#13133133 | C22 | semidirect |
| 20. M16×Dic53 | C22 | semidirect |
| 22. C2×#100×C53 | C22 | semidirect |
| 137. C2×Dic53 | #100 | semidirect |
| 170. #1783 | D53 | semidirect |
| 190. C2×#100 | C2×D53 | semidirect |
| 194. C53 | #21797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133213 | 2 |
| #20283344 | 2 |
| #20275553 | 2 |
| #20274636 | 2 |
| #20274635 | 2 |
| C53×#1783 | 2 |
| #21797 | 53 |