Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1030 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1030 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×#16811021 | C2 | semidirect |
| 3. C2×#16810996 | C2 | semidirect |
| 4. C2×#16810970 | C2 | semidirect |
| 5. #20274343 | C2 | direct (N × H) |
| 6. C2×C53×#322 | C2 | semidirect |
| 13. #16811021 | C22 | semidirect |
| 17. #16810996 | C22 | semidirect |
| 19. #16810970 | C22 | semidirect |
| 24. C53×#322 | C22 | semidirect |
| 76. C2×C8×C53 | SD16 | semidirect |
| 114. C8×C53 | C2×SD16 | semidirect |
| 135. C2×#322 | D53 | semidirect |
| 136. C2×C53 | #1715 | semidirect |
| 158. #322 | C2×D53 | semidirect |
| 159. C53 | C2×#1715 | semidirect |
| 213. C2×C8 | #11719913 | semidirect |
| 249. C8 | C2×#11719913 | semidirect |
| 266. C2 | #20274343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811021 | 2 |
| C2×#16811000 | 2 |
| C2×#16810996 | 2 |
| C2×#16810970 | 2 |
| #20274343 | 2 |
| C2×C53×#322 | 2 |
| C2×#1715 | 53 |