Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3950 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 3950 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×#6105 | C2 | semidirect |
| 2. C22×#88123 | C2 | semidirect |
| 3. C2×#11718737 | C2 | direct (N × H) |
| 4. C22×C4×#1055 | C2 | semidirect |
| 13. C22×#6105 | C22 | semidirect |
| 17. C2×#88123 | C22 | semidirect |
| 18. #11718737 | C22 | direct (N × H) |
| 19. C2×C4×#1055 | C22 | semidirect |
| 37. C2×#6105 | C23 | semidirect |
| 39. C22×#1055 | D4 | semidirect |
| 42. #88123 | C23 | semidirect |
| 43. C4×#1055 | C23 | semidirect |
| 55. C22×C4×C13 | SD16 | semidirect |
| 70. C2×#1055 | C2×D4 | semidirect |
| 88. C2×C4×C13 | C2×SD16 | semidirect |
| 97. #1055 | C22×D4 | semidirect |
| 115. C22×C13 | #492 | semidirect |
| 120. C4×C13 | C22×SD16 | semidirect |
| 148. C2×C13 | C2×#492 | semidirect |
| 167. C22×C4 | #6105 | semidirect |
| 178. C13 | C22×#492 | semidirect |
| 193. C2×C4 | C2×#6105 | semidirect |
| 203. C22 | #11718737 | direct (N × H) |
| 208. C4 | C22×#6105 | semidirect |
| 212. C2 | C2×#11718737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6105 | 2 |
| C22×#88123 | 2 |
| C2×#11718737 | 2 |
| C22×C4×#1055 | 2 |
| C22×C13×#127 | 2 |
| C22×#492 | 13 |