Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1722 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1722 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 |
|---|---|---|
| 2. C2×#16810995 | C2 | semidirect |
| 3. C2×#16810914 | C2 | semidirect |
| 4. #20273832 | C2 | direct (N × H) |
| 5. C2×#16810350 | C2 | semidirect |
| 6. C2×C53×#331 | C2 | semidirect |
| 12. C2×#13133217 | C22 | semidirect |
| 17. #16810995 | C22 | semidirect |
| 19. #16810914 | C22 | semidirect |
| 22. C2×C4×#88322 | C22 | semidirect |
| 23. #16810350 | C22 | semidirect |
| 25. C2×C4⋊C8×C53 | C22 | semidirect |
| 26. C53×#331 | C22 | semidirect |
| 41. #13133217 | C23 | semidirect |
| 57. C4×#88322 | C23 | semidirect |
| 66. C4⋊C8×C53 | C23 | semidirect |
| 90. C2×D212 | SD16 | semidirect |
| 144. D212 | C2×SD16 | semidirect |
| 175. C2×#331 | D53 | semidirect |
| 178. C2×C53 | #1629 | semidirect |
| 197. C2×C4⋊C8 | C2×D53 | semidirect |
| 200. #331 | C2×D53 | semidirect |
| 202. C53 | C2×#1629 | semidirect |
| 239. C4⋊C8 | C22×D53 | semidirect |
| 348. C2 | #20273832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811258 | 2 |
| C2×#16810995 | 2 |
| C2×#16810914 | 2 |
| #20273832 | 2 |
| C2×#16810350 | 2 |
| C2×C53×#331 | 2 |
| C2×#1629 | 53 |