Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#88124 | C2 | semidirect |
| 3. C2×#11718374 | C2 | direct (N × H) |
| 4. C22×#88061 | C2 | semidirect |
| 5. C22×C13×#97 | C2 | semidirect |
| 15. C2×#88124 | C22 | semidirect |
| 16. C2×C13×#97 | C22 | semidirect |
| 17. C2×#88061 | C22 | semidirect |
| 18. #11718374 | C22 | direct (N × H) |
| 38. #88124 | C23 | semidirect |
| 39. C13×#97 | C23 | semidirect |
| 40. #88061 | C23 | semidirect |
| 70. C22×#97 | D13 | semidirect |
| 102. C2×#97 | C2×D13 | semidirect |
| 103. C22×C13 | #490 | semidirect |
| 135. #97 | C22×D13 | semidirect |
| 136. C2×C13 | C2×#490 | semidirect |
| 164. C13 | C22×#490 | semidirect |
| 187. C22 | #11718374 | direct (N × H) |
| 196. C2 | C2×#11718374 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88128 | 2 |
| C22×#88124 | 2 |
| C2×#11718374 | 2 |
| C22×#88061 | 2 |
| C22×C13×#97 | 2 |
| C22×#490 | 13 |