Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. C2×#16810997 | C2 | semidirect |
| 2. C2×#16810818 | C2 | semidirect |
| 3. #20273798 | C2 | direct (N × H) |
| 4. C2×#16810372 | C2 | semidirect |
| 5. C2×D4⋊#88322 | C2 | semidirect |
| 6. C2×C53×#555 | C2 | semidirect |
| 11. #16810997 | C22 | semidirect |
| 13. #16810818 | C22 | semidirect |
| 17. #16810372 | C22 | semidirect |
| 18. D4⋊#88322 | C22 | semidirect |
| 21. C53×#555 | C22 | semidirect |
| 162. C2×#555 | D53 | semidirect |
| 169. C2×C53 | #1624 | semidirect |
| 177. #555 | C2×D53 | semidirect |
| 193. C53 | C2×#1624 | semidirect |
| 330. C2 | #20273798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810997 | 2 |
| C2×#16810818 | 2 |
| #20273798 | 2 |
| C2×#16810372 | 2 |
| C2×D4⋊#88322 | 2 |
| C2×C53×#555 | 2 |
| C2×#1624 | 53 |