Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11719171 | C2 | semidirect |
| 4. #11719150 | C2 | semidirect |
| 5. #11719135 | C2 | semidirect |
| 8. C23×#261 | C22 | semidirect |
| 9. C22×D4×C13 | C4 | semidirect |
| 10. C22×C22⋊D13 | C4 | semidirect |
| 11. C22×C22⋊D13 | C4 | semidirect |
| 13. C2×D4×D13 | C4 | semidirect |
| 15. C22×D52 | C4 | semidirect |
| 19. C2×C22⋊#261 | C22 | semidirect |
| 20. C2×C22⋊#261 | C22 | semidirect |
| 21. (C2×#261)⋊C4 | C22 | semidirect |
| 23. C24×C13 | C2×C4 | semidirect |
| 29. C23×D13 | C2×C4 | semidirect |
| 30. C23×D13 | C2×C4 | semidirect |
| 39. C2×D4×C13 | C2×C4 | semidirect |
| 40. C22×C4×C13 | C2×C4 | semidirect |
| 43. C2×C22⋊D13 | C2×C4 | semidirect |
| 44. C2×C22⋊D13 | C2×C4 | semidirect |
| 45. C22×Dic13 | C2×C4 | semidirect |
| 50. C2×D52 | C2×C4 | semidirect |
| 52. C2×C4×D13 | C2×C4 | semidirect |
| 61. C23×C13 | C22⋊C4 | semidirect |
| 77. C22×D13 | C22⋊C4 | semidirect |
| 78. C22×D13 | C22⋊C4 | semidirect |
| 140. C22×D4 | #261 | semidirect |
| 169. C24 | C2×#261 | semidirect |
| 180. C2×D4 | C2×#261 | semidirect |
| 188. C22×C4 | C2×#261 | semidirect |
| 192. C13 | #2308 | semidirect |
| 217. C23 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C22×C22⋊#261 | 2 |
| #11719171 | 2 |
| #11719150 | 2 |
| #11719135 | 2 |
| #2308 | 13 |