Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 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 |
|---|---|---|
| 2. C2×#16810418 | C2 | direct (N × H) |
| 7. #16810418 | C22 | direct (N × H) |
| 8. C23×Q8×C53 | C4 | semidirect |
| 11. C2×#124×C53 | C4 | semidirect |
| 14. C22×C42×C53 | C4 | semidirect |
| 24. C22×Q8×C53 | C2×C4 | semidirect |
| 35. #124×C53 | C2×C4 | semidirect |
| 40. C2×C42×C53 | C2×C4 | semidirect |
| 52. C2×Q8×C53 | C22×C4 | semidirect |
| 77. C42×C53 | C22×C4 | semidirect |
| 124. C22×C53 | #354 | semidirect |
| 140. C2×C53 | C2×#354 | semidirect |
| 142. C23×Q8 | Dic53 | semidirect |
| 145. C2×#124 | Dic53 | semidirect |
| 149. C22×C42 | Dic53 | semidirect |
| 153. C53 | C22×#354 | semidirect |
| 158. C22×Q8 | C2×Dic53 | semidirect |
| 170. #124 | C2×Dic53 | semidirect |
| 177. C2×C42 | C2×Dic53 | semidirect |
| 191. C2×Q8 | C22×Dic53 | semidirect |
| 218. C42 | C22×Dic53 | semidirect |
| 262. C22 | #16810418 | direct (N × H) |
| 275. C2 | C2×#16810418 | 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×#16810418 | 2 |
| C22×#124×C53 | 2 |
| C22×#354 | 53 |