Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 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. Q82×C13 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 6. Q8×#1055 | C2 | semidirect |
| 7. #11718681 | C2 | semidirect |
| 37. #6106 | Q8 | direct (N × H) |
| 47. Q8×C13 | SD16 | semidirect |
| 48. Q8×C13 | C2×Q8 | semidirect |
| 60. #1055 | C2×Q8 | semidirect |
| 61. Q82 | D13 | semidirect |
| 118. C13 | Q8×SD16 | semidirect |
| 123. Q8 | #6106 | direct (N × H) |
| 124. Q8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C13 | 2 |
| Q8×D52 | 2 |
| #11718745 | 2 |
| #11718740 | 2 |
| C4×#6106 | 2 |
| Q8×#1055 | 2 |
| #11718681 | 2 |
| Q8×SD16 | 13 |