Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
5758 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 5758 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×#6118 | C2 | semidirect |
| 2. C23×C4×#261 | C2 | semidirect |
| 3. C22×#88116 | C2 | direct (N × H) |
| 6. C23×D4×C13 | C4 | semidirect |
| 11. C22×#6129 | C4 | semidirect |
| 14. C23×Dic26 | C4 | semidirect |
| 17. C22×C4×#261 | C22 | semidirect |
| 19. C22×#6118 | C22 | semidirect |
| 20. C2×#88116 | C22 | direct (N × H) |
| 26. C22×D4×C13 | C2×C4 | semidirect |
| 37. C2×#6129 | C2×C4 | semidirect |
| 44. C22×Dic26 | C2×C4 | semidirect |
| 47. C2×C4×#261 | C23 | semidirect |
| 49. C2×#6118 | C23 | semidirect |
| 50. #88116 | C23 | direct (N × H) |
| 61. C2×D4×C13 | C22×C4 | semidirect |
| 74. #6129 | C22×C4 | semidirect |
| 82. C2×Dic26 | C22×C4 | semidirect |
| 85. C4×#261 | C24 | semidirect |
| 87. #6118 | C24 | semidirect |
| 94. C23×C13 | #104 | semidirect |
| 103. D4×C13 | C23×C4 | semidirect |
| 119. Dic26 | C23×C4 | semidirect |
| 127. C23×D4 | #261 | semidirect |
| 139. C22×C13 | C2×#104 | semidirect |
| 163. C22×D4 | C2×#261 | semidirect |
| 182. C2×C13 | C22×#104 | semidirect |
| 202. C2×D4 | C22×#261 | semidirect |
| 222. C13 | C23×#104 | semidirect |
| 229. C23 | #88116 | direct (N × H) |
| 236. D4 | C23×#261 | semidirect |
| 258. C22 | C2×#88116 | direct (N × H) |
| 269. C2 | C22×#88116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6118 | 2 |
| C23×C4×#261 | 2 |
| C22×#88116 | 2 |
| C23×#6129 | 2 |
| C23×#104 | 13 |