Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
4632 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1106 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. C24×#261 | C2 | semidirect |
| 3. C22×C22⋊#261 | C2 | direct (N × H) |
| 4. C25×C13 | C4 | semidirect |
| 6. C24×D13 | C4 | semidirect |
| 7. C24×D13 | C4 | semidirect |
| 11. C23×#261 | C22 | semidirect |
| 12. C2×C22⋊#261 | C22 | direct (N × H) |
| 15. C24×C13 | C2×C4 | semidirect |
| 20. C23×D13 | C2×C4 | semidirect |
| 21. C23×D13 | C2×C4 | semidirect |
| 26. C22×#261 | C23 | semidirect |
| 27. C22⋊#261 | C23 | direct (N × H) |
| 30. C23×C13 | C22⋊C4 | semidirect |
| 32. C23×C13 | C22×C4 | semidirect |
| 36. C22×D13 | C22⋊C4 | semidirect |
| 38. C22×D13 | C22×C4 | semidirect |
| 39. C22×D13 | C22×C4 | semidirect |
| 44. C2×#261 | C24 | semidirect |
| 49. C22×C13 | C2×C22⋊C4 | semidirect |
| 51. C22×C13 | C23×C4 | semidirect |
| 55. C2×D13 | C2×C22⋊C4 | semidirect |
| 57. C2×D13 | C23×C4 | semidirect |
| 66. C25 | #261 | semidirect |
| 71. C2×C13 | C22×C22⋊C4 | semidirect |
| 74. D13 | C22×C22⋊C4 | semidirect |
| 87. C24 | C2×#261 | semidirect |
| 91. C13 | C23×C22⋊C4 | semidirect |
| 103. C23 | C22⋊#261 | direct (N × H) |
| 105. C23 | C22×#261 | semidirect |
| 117. C22 | C2×C22⋊#261 | direct (N × H) |
| 119. C22 | C23×#261 | semidirect |
| 125. C2 | C22×C22⋊#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D13 | 2 |
| C24×#261 | 2 |
| C22×C22⋊#261 | 2 |
| C23×C22⋊C4 | 13 |