Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 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 |
|---|---|---|
| 2. Q8×#1055 | C2 | semidirect |
| 3. D4×#1055 | C2 | semidirect |
| 4. #11718586 | C2 | semidirect |
| 5. C2×C4×#1055 | C2 | semidirect |
| 19. C13×#41 | C8 | semidirect |
| 37. Q8×C13 | C2×C8 | semidirect |
| 38. D4×C13 | C2×C8 | semidirect |
| 41. C2×C4×C13 | C2×C8 | semidirect |
| 49. #1055 | #41 | direct (N × H) |
| 82. #41 | #1055 | direct (N × H) |
| 98. C13 | C8×#41 | semidirect |
| 100. Q8 | C2×#1055 | semidirect |
| 101. D4 | C2×#1055 | semidirect |
| 104. C2×C4 | C2×#1055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#41 | 2 |
| Q8×#1055 | 2 |
| D4×#1055 | 2 |
| #11718586 | 2 |
| C2×C4×#1055 | 2 |
| C8×#41 | 13 |