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. Q8×D52 | C2 | semidirect |
| 2. C8×Q8×C13 | C2 | semidirect |
| 3. #11718507 | C2 | semidirect |
| 5. #11718343 | C2 | semidirect |
| 29. D104 | Q8 | direct (N × H) |
| 32. Q8×C13 | D8 | semidirect |
| 38. D52 | C2×Q8 | semidirect |
| 42. C8×C13 | C2×Q8 | semidirect |
| 46. C8×Q8 | D13 | semidirect |
| 85. C13 | Q8×D8 | semidirect |
| 88. Q8 | D104 | direct (N × H) |
| 97. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| C8×Q8×C13 | 2 |
| #11718507 | 2 |
| C4×D104 | 2 |
| #11718343 | 2 |
| Q8×D8 | 13 |