Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4638 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 987 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×#6104 | C2 | semidirect |
| 2. C22×#88128 | C2 | semidirect |
| 3. C2×#11718734 | C2 | direct (N × H) |
| 4. C22×C4×#1055 | C2 | semidirect |
| 5. C22×C13×#127 | C2 | semidirect |
| 11. C2×C13×#127 | C22 | semidirect |
| 14. C22×#6104 | C22 | semidirect |
| 17. C2×#88128 | C22 | semidirect |
| 18. #11718734 | C22 | direct (N × H) |
| 19. C2×C4×#1055 | C22 | semidirect |
| 35. C13×#127 | C23 | semidirect |
| 39. C2×#6104 | C23 | semidirect |
| 40. C22×#1055 | D4 | semidirect |
| 43. #88128 | C23 | semidirect |
| 44. C4×#1055 | C23 | semidirect |
| 59. C22×C4×C13 | D8 | semidirect |
| 73. C2×#1055 | C2×D4 | semidirect |
| 77. C22×#127 | D13 | semidirect |
| 95. C2×C4×C13 | C2×D8 | semidirect |
| 103. #1055 | C22×D4 | semidirect |
| 114. C2×#127 | C2×D13 | semidirect |
| 121. C22×C13 | #493 | semidirect |
| 129. C4×C13 | C22×D8 | semidirect |
| 152. #127 | C22×D13 | semidirect |
| 157. C2×C13 | C2×#493 | semidirect |
| 180. C22×C4 | #6104 | semidirect |
| 190. C13 | C22×#493 | semidirect |
| 208. C2×C4 | C2×#6104 | semidirect |
| 221. C22 | #11718734 | direct (N × H) |
| 225. C4 | C22×#6104 | semidirect |
| 230. C2 | C2×#11718734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6104 | 2 |
| C22×#88128 | 2 |
| C2×#11718734 | 2 |
| C22×C4×#1055 | 2 |
| C22×C13×#127 | 2 |
| C22×#493 | 13 |