Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 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×C22⋊#261 | C2 | semidirect |
| 3. C2×#88119 | C2 | direct (N × H) |
| 4. C25×C13 | C4 | semidirect |
| 9. C22×C22⋊D13 | C4 | semidirect |
| 11. C23×Dic13 | C4 | semidirect |
| 13. C2×C22⋊#261 | C22 | semidirect |
| 14. #88119 | C22 | direct (N × H) |
| 19. C24×C13 | C2×C4 | semidirect |
| 31. C2×C22⋊D13 | C2×C4 | semidirect |
| 35. C22×Dic13 | C2×C4 | semidirect |
| 37. C22⋊#261 | C23 | semidirect |
| 48. C23×C13 | C22×C4 | semidirect |
| 65. C2×Dic13 | C22×C4 | semidirect |
| 75. C22×C13 | #99 | semidirect |
| 90. C25 | #261 | semidirect |
| 103. C2×C13 | C2×#99 | semidirect |
| 116. C24 | C2×#261 | semidirect |
| 130. C13 | C22×#99 | semidirect |
| 150. C23 | C22×#261 | semidirect |
| 172. C22 | #88119 | direct (N × H) |
| 183. C2 | C2×#88119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D13 | 2 |
| C22×C22⋊#261 | 2 |
| C2×#88119 | 2 |
| C22×#99 | 13 |