Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 4. #11718692 | C2 | semidirect |
| 5. C4×#6107 | C2 | semidirect |
| 6. #11718682 | C2 | semidirect |
| 74. C2×C4×C13 | Q16 | semidirect |
| 166. C13 | #3104 | semidirect |
| 181. C2×C4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C13 | 2 |
| #11719175 | 2 |
| #11718889 | 2 |
| #11718692 | 2 |
| C4×#6107 | 2 |
| #11718682 | 2 |
| #11718631 | 2 |
| #11718586 | 2 |
| #3104 | 13 |