Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #13114206 | C2 | semidirect |
| 4. #13112910 | C2 | semidirect |
| 5. #13112886 | C2 | semidirect |
| 7. Q8×C13×C16 | C2 | semidirect |
| 71. C13×C16 | SD16 | semidirect |
| 73. Q8×C16 | D13 | semidirect |
| 81. Q8×C13 | SD32 | semidirect |
| 179. C16 | #6106 | semidirect |
| 180. C13 | #12441 | semidirect |
| 185. Q8 | #88040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13117092 | 2 |
| #13114206 | 2 |
| #13114196 | 2 |
| #13112910 | 2 |
| #13112886 | 2 |
| #13112883 | 2 |
| Q8×C13×C16 | 2 |
| #12441 | 13 |