Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
534 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 94 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. Q8×#6122 | C2 | semidirect |
| 4. #13130164 | C2 | semidirect |
| 5. #13129706 | C2 | semidirect |
| 6. #13129681 | C2 | semidirect |
| 122. #6122 | SD16 | semidirect |
| 173. Q8×C13 | #100 | semidirect |
| 389. C13 | #9254 | semidirect |
| 405. Q8 | #88121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6122 | 2 |
| #13130978 | 2 |
| #13130343 | 2 |
| #13130164 | 2 |
| #13129706 | 2 |
| #13129681 | 2 |
| C2×#11718824 | 2 |
| #9254 | 13 |