Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #11718754 | C2 | semidirect |
| 4. #11718753 | C2 | semidirect |
| 6. #11718692 | C2 | semidirect |
| 64. C2×C4×C13 | Q16 | semidirect |
| 148. C13 | #3209 | semidirect |
| 160. C2×C4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×#88123 | 2 |
| #11718754 | 2 |
| #11718753 | 2 |
| #11718711 | 2 |
| #11718692 | 2 |
| #11718586 | 2 |
| #3209 | 13 |