Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C24×Dic26 | C2 | semidirect |
| 3. C22×#88129 | C2 | direct (N × H) |
| 4. C23×#6103 | C2 | semidirect |
| 5. C23×C42×C13 | C2 | semidirect |
| 13. C23×Dic26 | C22 | semidirect |
| 14. C22×C42×C13 | C22 | semidirect |
| 15. C22×#6103 | C22 | semidirect |
| 16. C2×#88129 | C22 | direct (N × H) |
| 30. C22×Dic26 | C23 | semidirect |
| 31. C2×C42×C13 | C23 | semidirect |
| 32. C2×#6103 | C23 | semidirect |
| 33. #88129 | C23 | direct (N × H) |
| 51. C2×Dic26 | C24 | semidirect |
| 52. C42×C13 | C24 | semidirect |
| 53. #6103 | C24 | semidirect |
| 58. C23×C42 | D13 | semidirect |
| 59. C23×C13 | #124 | semidirect |
| 85. C22×C42 | C2×D13 | semidirect |
| 86. C22×C13 | C2×#124 | semidirect |
| 112. C2×C42 | C22×D13 | semidirect |
| 113. C2×C13 | C22×#124 | semidirect |
| 135. C42 | C23×D13 | semidirect |
| 136. C13 | C23×#124 | semidirect |
| 141. C23 | #88129 | direct (N × H) |
| 156. C22 | C2×#88129 | direct (N × H) |
| 164. C2 | C22×#88129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic26 | 2 |
| C24×D52 | 2 |
| C22×#88129 | 2 |
| C23×#6103 | 2 |
| C23×C42×C13 | 2 |
| C23×#124 | 13 |