Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
| 4. C2×C4⋊#1057 | C2 | semidirect |
| 6. #11718290 | C2 | semidirect |
| 7. #11718290 | C2 | semidirect |
| 71. C2×C4×C13 | M16 | semidirect |
| 84. C2×Dic13 | M16 | semidirect |
| 182. C13 | #1851 | semidirect |
| 215. C2×C4 | #6122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6122 | 2 |
| C2×C22⋊#1057 | 2 |
| C2×#88112 | 2 |
| C2×C4⋊#1057 | 2 |
| C22⋊C4×Dic13 | 2 |
| #11718290 | 2 |
| #1851 | 13 |