Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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. D4×Q8×C13 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. #11718748 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. Q8×#1055 | C2 | semidirect |
| 7. #11718668 | C2 | semidirect |
| 38. #6104 | Q8 | direct (N × H) |
| 48. Q8×C13 | D8 | semidirect |
| 50. D4×C13 | C2×Q8 | semidirect |
| 58. D52 | C2×Q8 | semidirect |
| 62. #1055 | C2×Q8 | semidirect |
| 64. D4×Q8 | D13 | semidirect |
| 124. C13 | Q8×D8 | semidirect |
| 129. Q8 | #6104 | direct (N × H) |
| 133. D4 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| Q8×D52 | 2 |
| #11718748 | 2 |
| #11718739 | 2 |
| Q8×#1055 | 2 |
| C4×#6104 | 2 |
| #11718668 | 2 |
| Q8×D8 | 13 |