Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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. C2×#88112 | C2 | semidirect |
| 5. C2×C4⋊#1057 | C2 | semidirect |
| 6. #11719079 | C2 | direct (N × H) |
| 21. #88112 | C22 | semidirect |
| 22. C4⋊#1057 | C22 | semidirect |
| 103. C2×C13 | #424 | semidirect |
| 130. C13 | C2×#424 | semidirect |
| 167. C2 | #11719079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6118 | 2 |
| C22×D13⋊C8 | 2 |
| C2×#88146 | 2 |
| C2×#88112 | 2 |
| C2×C4⋊#1057 | 2 |
| #11719079 | 2 |
| C2×#424 | 13 |