Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 2. C22×#6122 | C2 | semidirect |
| 3. #11719126 | C2 | direct (N × H) |
| 4. C2×#88111 | C2 | semidirect |
| 14. C2×#6122 | C22 | semidirect |
| 15. C22×#1057 | C22 | semidirect |
| 16. #88111 | C22 | semidirect |
| 39. C2×#1057 | C23 | semidirect |
| 50. C22×D13 | M16 | semidirect |
| 80. C2×D13 | C2×M16 | semidirect |
| 98. C2×C13 | #407 | semidirect |
| 125. C13 | C2×#407 | semidirect |
| 168. C2 | #11719126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D13 | 2 |
| C22×#6122 | 2 |
| #11719126 | 2 |
| C2×#88111 | 2 |
| C2×#407 | 13 |