Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4638 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 1067 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×D104 | C2 | semidirect |
| 2. C22×#88128 | C2 | semidirect |
| 3. C2×#11718356 | C2 | direct (N × H) |
| 4. C22×C4×C8×C13 | C2 | semidirect |
| 10. C22×D104 | C22 | semidirect |
| 12. C2×#88128 | C22 | semidirect |
| 13. C2×C4×C8×C13 | C22 | semidirect |
| 14. #11718356 | C22 | direct (N × H) |
| 23. C22×C8×C13 | D4 | semidirect |
| 28. C2×D104 | C23 | semidirect |
| 30. #88128 | C23 | semidirect |
| 31. C4×C8×C13 | C23 | semidirect |
| 37. C22×C4×C13 | D8 | semidirect |
| 48. C2×C8×C13 | C2×D4 | semidirect |
| 56. C22×C4×C8 | D13 | semidirect |
| 65. C2×C4×C13 | C2×D8 | semidirect |
| 73. C8×C13 | C22×D4 | semidirect |
| 83. C2×C4×C8 | C2×D13 | semidirect |
| 84. C22×C13 | #493 | semidirect |
| 92. C4×C13 | C22×D8 | semidirect |
| 104. C22×C8 | D52 | semidirect |
| 110. C4×C8 | C22×D13 | semidirect |
| 111. C2×C13 | C2×#493 | semidirect |
| 125. C22×C4 | D104 | semidirect |
| 131. C2×C8 | C2×D52 | semidirect |
| 135. C13 | C22×#493 | semidirect |
| 147. C2×C4 | C2×D104 | semidirect |
| 152. C8 | C22×D52 | semidirect |
| 156. C22 | #11718356 | direct (N × H) |
| 161. C4 | C22×D104 | semidirect |
| 164. C2 | C2×#11718356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D104 | 2 |
| C22×#88128 | 2 |
| C2×#11718356 | 2 |
| C22×C4×C8×C13 | 2 |
| C22×#493 | 13 |