Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
786 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 296 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. #13130889 | C2 | semidirect |
| 3. #13130763 | C2 | semidirect |
| 4. C4⋊C4×#1057 | C2 | semidirect |
| 6. C42×#1057 | C2 | semidirect |
| 31. C13×#126 | C8 | semidirect |
| 68. C13×C4⋊C4 | C2×C8 | semidirect |
| 70. C42×C13 | C2×C8 | semidirect |
| 109. #1057 | #126 | direct (N × H) |
| 146. #126 | #1057 | direct (N × H) |
| 187. C4⋊C4 | C2×#1057 | semidirect |
| 195. C42 | C2×#1057 | 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 |
|---|---|
| #13130905 | 2 |
| #13130889 | 2 |
| #13130763 | 2 |
| C4⋊C4×#1057 | 2 |
| C22⋊C4×#1057 | 2 |
| C42×#1057 | 2 |
| #126×Dic13 | 2 |
| C8×#126 | 13 |