Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. C2×C13×C4⋊Q8 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718748 | C2 | semidirect |
| 6. #11718745 | C2 | semidirect |
| 8. #11718625 | C2 | semidirect |
| 9. #11718585 | C2 | semidirect |
| 44. #6127 | Q8 | semidirect |
| 92. D52 | C2×Q8 | semidirect |
| 97. Dic26 | C2×Q8 | semidirect |
| 99. C2×C4⋊Q8 | D13 | semidirect |
| 191. C13 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C4⋊Q8 | 2 |
| C4×#6127 | 2 |
| #11718755 | 2 |
| #11718752 | 2 |
| #11718748 | 2 |
| #11718745 | 2 |
| #11718627 | 2 |
| #11718625 | 2 |
| #11718585 | 2 |
| #3079 | 13 |