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×#16810910 | C2 | semidirect |
| 3. #20273829 | C2 | direct (N × H) |
| 4. C2×#16810367 | C2 | semidirect |
| 5. C2×#16810352 | C2 | semidirect |
| 6. C2×C53×#492 | C2 | semidirect |
| 15. #16810910 | C22 | semidirect |
| 17. C2×C4⋊#88322 | C22 | semidirect |
| 19. #16810367 | C22 | semidirect |
| 20. #16810352 | C22 | semidirect |
| 22. C2×C4⋊Q8×C53 | C22 | semidirect |
| 25. C53×#492 | C22 | semidirect |
| 26. C2×C4×C8×C53 | C22 | semidirect |
| 49. C4⋊#88322 | C23 | semidirect |
| 59. C4⋊Q8×C53 | C23 | semidirect |
| 66. C4×C8×C53 | C23 | semidirect |
| 93. C2×D212 | SD16 | semidirect |
| 146. D212 | C2×SD16 | semidirect |
| 172. C2×#492 | D53 | semidirect |
| 178. C2×C53 | #1629 | semidirect |
| 187. C2×C4⋊Q8 | C2×D53 | semidirect |
| 193. #492 | C2×D53 | semidirect |
| 199. C2×C4×C8 | C2×D53 | semidirect |
| 202. C53 | C2×#1629 | semidirect |
| 220. C4⋊Q8 | C22×D53 | semidirect |
| 242. C4×C8 | C22×D53 | semidirect |
| 348. C2 | #20273829 | 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×#16810910 | 2 |
| #20273829 | 2 |
| C2×#16810367 | 2 |
| C2×#16810352 | 2 |
| C2×C53×#492 | 2 |
| C2×#1629 | 53 |