Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
570 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 270 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 |
| 2. #13131215 | C2 | semidirect |
| 3. #13131195 | C2 | semidirect |
| 4. D13⋊(C4⋊C16) | C2 | semidirect |
| 40. #6131 | C16 | semidirect |
| 67. Q8×C13 | C2×C16 | semidirect |
| 74. D52 | C2×C16 | semidirect |
| 78. C4×D13 | C2×C16 | semidirect |
| 153. C13 | #33502 | semidirect |
| 155. Q8 | D13⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6092 | 2 |
| #13131215 | 2 |
| #13131195 | 2 |
| D13⋊(C4⋊C16) | 2 |
| C8×#6131 | 2 |
| #33502 | 13 |