Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#88101 | C2 | semidirect |
| 3. C2×#88098 | C2 | semidirect |
| 4. #11718275 | C2 | direct (N × H) |
| 7. C2×C13×D8 | C4 | semidirect |
| 11. #88166 | C4 | semidirect |
| 13. C2×Dic52 | C4 | semidirect |
| 17. #88101 | C22 | semidirect |
| 19. #88098 | C22 | semidirect |
| 33. C13×D8 | C2×C4 | semidirect |
| 39. Dic52 | C2×C4 | semidirect |
| 92. C2×D8 | #261 | semidirect |
| 101. C2×C13 | #360 | semidirect |
| 120. D8 | C2×#261 | semidirect |
| 130. C13 | C2×#360 | semidirect |
| 169. C2 | #11718275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88166 | 2 |
| C2×#88101 | 2 |
| C2×#88098 | 2 |
| #11718275 | 2 |
| C2×#360 | 13 |