Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1350 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 459 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. C42×D52 | C2 | semidirect |
| 3. C4×#88058 | C2 | semidirect |
| 4. C4×#88061 | C2 | semidirect |
| 5. C42×C8×C13 | C2 | semidirect |
| 16. C4×D104 | C4 | direct (N × H) |
| 30. C4×D52 | C2×C4 | semidirect |
| 33. C4×C8×C13 | C2×C4 | semidirect |
| 35. #88061 | C2×C4 | semidirect |
| 36. #88058 | C2×C4 | semidirect |
| 52. C42×C13 | D8 | semidirect |
| 59. D104 | C42 | direct (N × H) |
| 64. C42×C8 | D13 | semidirect |
| 80. D52 | C2×C42 | semidirect |
| 83. C8×C13 | C2×C42 | semidirect |
| 103. C4×C13 | C4×D8 | semidirect |
| 124. C4×C8 | C4×D13 | semidirect |
| 149. C42 | D104 | direct (N × H) |
| 152. C13 | C42×D8 | semidirect |
| 171. C8 | C42×D13 | semidirect |
| 180. C4 | C4×D104 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D104 | 2 |
| C42×D52 | 2 |
| C4×#88058 | 2 |
| C4×#88061 | 2 |
| C42×C8×C13 | 2 |
| C42×D8 | 13 |