Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. M32×#6157 | C2 | semidirect |
| 4. #108×#6157 | C2 | semidirect |
| 5. #20289791 | C2 | semidirect |
| 6. #20289790 | C2 | semidirect |
| 19. #16811541 | C4 | semidirect |
| 26. #16810437 | C4 | semidirect |
| 27. #16810436 | C4 | semidirect |
| 28. #16810435 | C4 | semidirect |
| 29. C53×#361 | C4 | semidirect |
| 40. #13133292 | C2×C4 | semidirect |
| 44. #13133287 | C2×C4 | semidirect |
| 64. #13133157 | C2×C4 | semidirect |
| 67. #13133153 | C2×C4 | semidirect |
| 70. M32×C53 | C2×C4 | semidirect |
| 71. #108×C53 | C2×C4 | semidirect |
| 176. #6157 | #361 | direct (N × H) |
| 213. #361 | #6157 | direct (N × H) |
| 217. C53 | C4×#361 | semidirect |
| 242. M32 | C2×#6157 | semidirect |
| 249. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#6157 | 2 |
| D53⋊#361 | 2 |
| M32×#6157 | 2 |
| #108×#6157 | 2 |
| #20289791 | 2 |
| #20289790 | 2 |
| #361×D53 | 2 |
| C4×#361 | 53 |