Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1838 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1838 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×#16811258 | C2 | semidirect |
| 2. C2×#16810815 | C2 | semidirect |
| 3. #20273767 | C2 | direct (N × H) |
| 4. C2×#16810367 | C2 | semidirect |
| 5. C2×#16810352 | C2 | semidirect |
| 6. C2×C53×#493 | C2 | semidirect |
| 11. #16811258 | C22 | semidirect |
| 16. #16810815 | C22 | semidirect |
| 17. C2×C4⋊#88322 | C22 | semidirect |
| 19. #16810367 | C22 | semidirect |
| 20. #16810352 | C22 | semidirect |
| 23. C2×#127×C53 | C22 | semidirect |
| 25. C53×#493 | C22 | semidirect |
| 26. C2×C4×C8×C53 | C22 | semidirect |
| 50. C4⋊#88322 | C23 | semidirect |
| 64. #127×C53 | C23 | semidirect |
| 67. C4×C8×C53 | C23 | semidirect |
| 98. C2×D212 | D8 | semidirect |
| 154. D212 | C2×D8 | semidirect |
| 182. C2×#493 | D53 | semidirect |
| 189. C2×C53 | #1619 | semidirect |
| 200. C2×#127 | C2×D53 | semidirect |
| 205. #493 | C2×D53 | semidirect |
| 210. C2×C4×C8 | C2×D53 | semidirect |
| 213. C53 | C2×#1619 | semidirect |
| 237. #127 | C22×D53 | semidirect |
| 254. C4×C8 | C22×D53 | semidirect |
| 370. C2 | #20273767 | 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×#16810815 | 2 |
| #20273767 | 2 |
| C2×#16810367 | 2 |
| C2×#16810352 | 2 |
| C2×C53×#493 | 2 |
| C2×#1619 | 53 |