Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×#88112 | C2 | semidirect |
| 5. #11718290 | C2 | semidirect |
| 36. C22⋊Dic13 | C8 | semidirect |
| 56. C2×Dic13 | C2×C8 | semidirect |
| 73. C22×C13 | C4⋊C8 | semidirect |
| 124. C13 | #1850 | semidirect |
| 153. C22 | #88112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1057 | 2 |
| C2×C22⋊#1057 | 2 |
| C2×#88112 | 2 |
| C22⋊C4×Dic13 | 2 |
| #11718290 | 2 |
| #1850 | 13 |