Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
786 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 256 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. #13130891 | C2 | semidirect |
| 3. #13130763 | C2 | semidirect |
| 4. #13130628 | C2 | semidirect |
| 6. C42×#1057 | C2 | semidirect |
| 39. #88130 | C8 | semidirect |
| 68. C42×C13 | C2×C8 | semidirect |
| 72. #6101 | C2×C8 | semidirect |
| 109. #1057 | #126 | semidirect |
| 195. C42 | D13⋊C8 | semidirect |
| 196. C13 | C8×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13130907 | 2 |
| #13130891 | 2 |
| #13130763 | 2 |
| #13130628 | 2 |
| #13130570 | 2 |
| C42×#1057 | 2 |
| #13117384 | 2 |
| C8×#126 | 13 |