Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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. D8×#1055 | C2 | semidirect |
| 2. #13112908 | C2 | semidirect |
| 3. #13112797 | C2 | semidirect |
| 4. C16×#1055 | C2 | semidirect |
| 19. C13×D16 | C8 | semidirect |
| 34. C13×D8 | C2×C8 | semidirect |
| 46. C13×C16 | C2×C8 | semidirect |
| 68. #1055 | D16 | direct (N × H) |
| 92. D16 | #1055 | direct (N × H) |
| 110. D8 | C2×#1055 | semidirect |
| 123. C16 | C2×#1055 | semidirect |
| 124. C13 | C8×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#1055 | 2 |
| #13112908 | 2 |
| #13112797 | 2 |
| C16×#1055 | 2 |
| C4×C13×D16 | 2 |
| C8×D16 | 13 |