Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2062 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 331 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. C22×#13133132 | C2 | semidirect |
| 2. C2×#16810416 | C2 | direct (N × H) |
| 6. C2×#13133132 | C22 | semidirect |
| 7. #16810416 | C22 | direct (N × H) |
| 9. C23×D4×C53 | C4 | semidirect |
| 12. C2×#127×C53 | C4 | semidirect |
| 14. C22×C42×C53 | C4 | semidirect |
| 19. #13133132 | C23 | semidirect |
| 31. C22×D4×C53 | C2×C4 | semidirect |
| 38. #127×C53 | C2×C4 | semidirect |
| 41. C2×C42×C53 | C2×C4 | semidirect |
| 69. C2×D4×C53 | C22×C4 | semidirect |
| 81. C42×C53 | C22×C4 | semidirect |
| 137. C22×C53 | #353 | semidirect |
| 153. C2×C53 | C2×#353 | semidirect |
| 156. C23×D4 | Dic53 | semidirect |
| 159. C2×#127 | Dic53 | semidirect |
| 162. C22×C42 | Dic53 | semidirect |
| 166. C53 | C22×#353 | semidirect |
| 178. C22×D4 | C2×Dic53 | semidirect |
| 186. #127 | C2×Dic53 | semidirect |
| 191. C2×C42 | C2×Dic53 | semidirect |
| 221. C2×D4 | C22×Dic53 | semidirect |
| 235. C42 | C22×Dic53 | semidirect |
| 288. C22 | #16810416 | direct (N × H) |
| 301. C2 | C2×#16810416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133132 | 2 |
| C2×#16810416 | 2 |
| C22×#127×C53 | 2 |
| C22×#353 | 53 |