Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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. C23×#6104 | C2 | semidirect |
| 3. C22×#88129 | C2 | semidirect |
| 4. C2×#11718735 | C2 | direct (N × H) |
| 5. C22×#88043 | C2 | semidirect |
| 6. C22×C13×#127 | C2 | semidirect |
| 12. C2×C13×#127 | C22 | semidirect |
| 15. C22×#6105 | C22 | semidirect |
| 17. C22×#6104 | C22 | semidirect |
| 21. C2×#88129 | C22 | semidirect |
| 22. #11718735 | C22 | direct (N × H) |
| 23. C2×#88043 | C22 | semidirect |
| 42. C13×#127 | C23 | semidirect |
| 46. C2×#6105 | C23 | semidirect |
| 48. C2×#6104 | C23 | semidirect |
| 50. C22×#1055 | D4 | semidirect |
| 53. #88129 | C23 | semidirect |
| 54. #88043 | C23 | semidirect |
| 90. C2×#1055 | C2×D4 | semidirect |
| 94. C22×#127 | D13 | semidirect |
| 125. #1055 | C22×D4 | semidirect |
| 136. C2×#127 | C2×D13 | semidirect |
| 146. C22×C13 | #496 | semidirect |
| 181. #127 | C22×D13 | semidirect |
| 189. C2×C13 | C2×#496 | semidirect |
| 229. C13 | C22×#496 | semidirect |
| 264. C22 | #11718735 | direct (N × H) |
| 274. C2 | C2×#11718735 | 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 |
| C23×#6104 | 2 |
| C22×#88129 | 2 |
| C2×#11718735 | 2 |
| C22×#88043 | 2 |
| C22×C13×#127 | 2 |
| C22×#496 | 13 |