Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. C22×#6122 | C2 | semidirect |
| 3. C2×#88121 | C2 | semidirect |
| 4. #11719169 | C2 | semidirect |
| 5. #11718291 | C2 | semidirect |
| 52. #6122 | D4 | semidirect |
| 120. C22×C13 | #100 | semidirect |
| 198. C13 | #1900 | semidirect |
| 255. C22 | #88121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6122 | 2 |
| C2×#88193 | 2 |
| C2×#88121 | 2 |
| #11719169 | 2 |
| #11718291 | 2 |
| #1900 | 13 |