Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
248 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 248 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. #13114196 | C2 | semidirect |
| 3. #13112908 | C2 | semidirect |
| 4. #13112883 | C2 | semidirect |
| 5. Q8×C13×C16 | C2 | semidirect |
| 52. C13×C16 | SD16 | semidirect |
| 54. Q8×C16 | D13 | semidirect |
| 60. Q8×C13 | D16 | semidirect |
| 136. C16 | #6106 | semidirect |
| 137. C13 | #12439 | semidirect |
| 140. Q8 | D208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13117086 | 2 |
| #13114196 | 2 |
| #13112908 | 2 |
| #13112883 | 2 |
| Q8×C13×C16 | 2 |
| #12439 | 13 |