Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2078 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 627 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×Dic104 | C2 | semidirect |
| 3. C22×#88069 | C2 | semidirect |
| 4. C2×D13×Q32 | C2 | direct (N × H) |
| 6. C22×C13×Q32 | C2 | semidirect |
| 14. C2×C13×Q32 | C22 | semidirect |
| 16. C2×#88069 | C22 | semidirect |
| 18. D13×Q32 | C22 | direct (N × H) |
| 19. C2×Dic104 | C22 | semidirect |
| 39. C13×Q32 | C23 | semidirect |
| 41. #88069 | C23 | semidirect |
| 43. Dic104 | C23 | semidirect |
| 77. C22×Q32 | D13 | direct (N × H) |
| 80. C22×D13 | Q32 | direct (N × H) |
| 108. C2×Q32 | C2×D13 | direct (N × H) |
| 112. C22×C13 | C2×Q32 | semidirect |
| 114. C2×D13 | C2×Q32 | direct (N × H) |
| 141. Q32 | C22×D13 | direct (N × H) |
| 145. C2×C13 | C22×Q32 | semidirect |
| 147. D13 | C22×Q32 | direct (N × H) |
| 175. C13 | C23×Q32 | semidirect |
| 197. C22 | D13×Q32 | direct (N × H) |
| 205. C2 | C2×D13×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×D13 | 2 |
| C22×Dic104 | 2 |
| C22×#88069 | 2 |
| C2×D13×Q32 | 2 |
| C22×C16×D13 | 2 |
| C22×C13×Q32 | 2 |
| C23×Q32 | 13 |