Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 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 |
| 4. #11718886 | C2 | semidirect |
| 5. #11718751 | C2 | semidirect |
| 6. #11718744 | C2 | semidirect |
| 7. #11718585 | C2 | semidirect |
| 82. C2×C4⋊Q8 | D13 | semidirect |
| 96. C4×C13 | #137 | semidirect |
| 153. C13 | #3039 | semidirect |
| 188. C4 | #88196 | 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 |
| C2×#88196 | 2 |
| C4×#6127 | 2 |
| #11718886 | 2 |
| #11718751 | 2 |
| #11718744 | 2 |
| #11718585 | 2 |
| #3039 | 13 |