Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1146 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 267 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×#16811000 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810996 | C2 | semidirect |
| 4. C2×#16810970 | C2 | semidirect |
| 5. #20274381 | C2 | direct (N × H) |
| 6. C2×C53×#322 | C2 | semidirect |
| 15. #16811000 | C22 | semidirect |
| 16. #16811000 | C22 | semidirect |
| 18. #16810996 | C22 | semidirect |
| 20. #16810970 | C22 | semidirect |
| 24. C53×#322 | C22 | semidirect |
| 80. C2×C8×C53 | D8 | semidirect |
| 120. C8×C53 | C2×D8 | semidirect |
| 142. C2×#322 | D53 | semidirect |
| 143. C2×C53 | #1721 | semidirect |
| 165. #322 | C2×D53 | semidirect |
| 166. C53 | C2×#1721 | semidirect |
| 225. C2×C8 | D424 | semidirect |
| 262. C8 | C2×D424 | semidirect |
| 280. C2 | #20274381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810996 | 2 |
| C2×#16810970 | 2 |
| #20274381 | 2 |
| C2×C53×#322 | 2 |
| C2×#1721 | 53 |