Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
7902 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7902 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×C22⋊#261 | C2 | semidirect |
| 2. C22×#88119 | C2 | direct (N × H) |
| 4. C26×C13 | C4 | semidirect |
| 9. C23×C22⋊D13 | C4 | semidirect |
| 11. C24×Dic13 | C4 | semidirect |
| 13. C22×C22⋊#261 | C22 | semidirect |
| 14. C2×#88119 | C22 | direct (N × H) |
| 19. C25×C13 | C2×C4 | semidirect |
| 31. C22×C22⋊D13 | C2×C4 | semidirect |
| 35. C23×Dic13 | C2×C4 | semidirect |
| 37. C2×C22⋊#261 | C23 | semidirect |
| 38. #88119 | C23 | direct (N × H) |
| 49. C24×C13 | C22×C4 | semidirect |
| 66. C2×C22⋊D13 | C22×C4 | semidirect |
| 70. C22×Dic13 | C22×C4 | semidirect |
| 72. C22⋊#261 | C24 | semidirect |
| 83. C23×C13 | #99 | semidirect |
| 87. C23×C13 | C23×C4 | semidirect |
| 106. C2×Dic13 | C23×C4 | semidirect |
| 108. C26 | #261 | semidirect |
| 124. C22×C13 | C2×#99 | semidirect |
| 147. C25 | C2×#261 | semidirect |
| 165. C2×C13 | C22×#99 | semidirect |
| 188. C24 | C22×#261 | semidirect |
| 202. C13 | C23×#99 | semidirect |
| 222. C23 | #88119 | direct (N × H) |
| 226. C23 | C23×#261 | semidirect |
| 248. C22 | C2×#88119 | direct (N × H) |
| 259. C2 | C22×#88119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊#261 | 2 |
| C22×#88119 | 2 |
| C24×C22⋊D13 | 2 |
| C23×#99 | 13 |