Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #13127842 | C2 | semidirect |
| 3. #13117064 | C2 | semidirect |
| 4. #13116979 | C2 | semidirect |
| 7. Q8×C13×C16 | C2 | semidirect |
| 77. Q8×C16 | D13 | semidirect |
| 80. Q8×C13 | SD32 | semidirect |
| 174. C13 | #33926 | semidirect |
| 179. Q8 | #88040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127842 | 2 |
| Q8×D104 | 2 |
| #13117064 | 2 |
| #13116979 | 2 |
| #13116882 | 2 |
| C4×#88040 | 2 |
| Q8×C13×C16 | 2 |
| #33926 | 13 |