Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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×C4×#261 | C2 | semidirect |
| 3. C22×#6118 | C2 | semidirect |
| 4. C2×#88118 | C2 | direct (N × H) |
| 6. C22×Q8×C13 | C4 | semidirect |
| 9. C2×#6131 | C4 | semidirect |
| 12. C22×D52 | C4 | semidirect |
| 17. C2×C4×#261 | C22 | semidirect |
| 19. C2×#6118 | C22 | semidirect |
| 20. #88118 | C22 | direct (N × H) |
| 26. C2×Q8×C13 | C2×C4 | semidirect |
| 33. #6131 | C2×C4 | semidirect |
| 38. C2×D52 | C2×C4 | semidirect |
| 47. C4×#261 | C23 | semidirect |
| 49. #6118 | C23 | semidirect |
| 60. Q8×C13 | C22×C4 | semidirect |
| 69. D52 | C22×C4 | semidirect |
| 82. C22×C13 | #104 | semidirect |
| 100. C22×Q8 | #261 | semidirect |
| 112. C2×C13 | C2×#104 | semidirect |
| 125. C2×Q8 | C2×#261 | semidirect |
| 146. C13 | C22×#104 | semidirect |
| 154. Q8 | C22×#261 | semidirect |
| 180. C22 | #88118 | direct (N × H) |
| 191. C2 | C2×#88118 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C22×C4×#261 | 2 |
| C22×#6118 | 2 |
| C2×#88118 | 2 |
| C22×#104 | 13 |