Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
232 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 102 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×#6092 | C2 | semidirect |
| 3. #13129865 | C2 | semidirect |
| 4. Q8⋊#6092 | C2 | semidirect |
| 6. #13129749 | C2 | semidirect |
| 48. C13×SD16 | C16 | semidirect |
| 78. Q8×C13 | C2×C16 | semidirect |
| 90. C8×C13 | C2×C16 | semidirect |
| 152. SD16 | #6092 | semidirect |
| 173. C13 | SD16⋊C16 | semidirect |
| 176. Q8 | C2×#6092 | semidirect |
| 194. C8 | C2×#6092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6092 | 2 |
| D4×#6092 | 2 |
| #13129865 | 2 |
| Q8⋊#6092 | 2 |
| D4⋊#6092 | 2 |
| #13129749 | 2 |
| SD16×#1055 | 2 |
| SD16⋊C16 | 13 |