Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 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. C2×#11718729 | C2 | direct (N × H) |
| 3. C22×#88050 | C2 | semidirect |
| 5. C22×C4×#1055 | C2 | semidirect |
| 6. C22×C13×#125 | C2 | semidirect |
| 10. C2×C13×#125 | C22 | semidirect |
| 18. #11718729 | C22 | direct (N × H) |
| 19. C2×#88050 | C22 | semidirect |
| 21. C2×C4×#1055 | C22 | semidirect |
| 34. C13×#125 | C23 | semidirect |
| 45. #88050 | C23 | semidirect |
| 47. C4×#1055 | C23 | semidirect |
| 78. C22×#125 | D13 | semidirect |
| 110. C2×#125 | C2×D13 | semidirect |
| 121. C22×C13 | #488 | semidirect |
| 147. #125 | C22×D13 | semidirect |
| 159. C2×C13 | C2×#488 | semidirect |
| 192. C13 | C22×#488 | semidirect |
| 218. C22 | #11718729 | direct (N × H) |
| 228. C2 | C2×#11718729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88129 | 2 |
| C2×#11718729 | 2 |
| C22×#88050 | 2 |
| C22×#88049 | 2 |
| C22×C4×#1055 | 2 |
| C22×C13×#125 | 2 |
| C22×#488 | 13 |