Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1880 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 810 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 |
|---|---|---|
| 3. C2×#88237 | C2 | direct (N × H) |
| 4. C22×C4⋊#261 | C2 | semidirect |
| 5. C22×C4×#261 | C2 | semidirect |
| 8. C23×C4×C13 | C4 | semidirect |
| 9. C23×Dic13 | C4 | semidirect |
| 10. C22×C4×D13 | C4 | semidirect |
| 11. C22×C4×D13 | C4 | semidirect |
| 12. C22×C4×D13 | C4 | semidirect |
| 17. #88237 | C22 | direct (N × H) |
| 18. C2×C4⋊#261 | C22 | semidirect |
| 19. C2×C4×#261 | C22 | semidirect |
| 30. C22×C4×C13 | C2×C4 | semidirect |
| 33. C22×Dic13 | C2×C4 | semidirect |
| 36. C2×C4×D13 | C2×C4 | semidirect |
| 37. C2×C4×D13 | C2×C4 | semidirect |
| 38. C2×C4×D13 | C2×C4 | semidirect |
| 43. C4⋊#261 | C23 | semidirect |
| 44. C4×#261 | C23 | semidirect |
| 62. C2×C4×C13 | C22×C4 | semidirect |
| 65. C2×Dic13 | C22×C4 | semidirect |
| 68. C4×D13 | C22×C4 | semidirect |
| 69. C4×D13 | C22×C4 | semidirect |
| 78. C22×C13 | #117 | semidirect |
| 84. C2×D13 | #117 | semidirect |
| 103. C23×C4 | #261 | semidirect |
| 109. C2×C13 | C2×#117 | semidirect |
| 112. D13 | C2×#117 | semidirect |
| 135. C22×C4 | C2×#261 | semidirect |
| 139. C13 | C22×#117 | semidirect |
| 165. C2×C4 | C22×#261 | semidirect |
| 175. C22 | #88237 | direct (N × H) |
| 187. C2 | C2×#88237 | 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×C22⋊#261 | 2 |
| C2×#88237 | 2 |
| C22×C4⋊#261 | 2 |
| C22×C4×#261 | 2 |
| C22×#117 | 13 |