Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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 |
|---|---|---|
| 1. C24×C4×C13 | C2 | semidirect |
| 3. C22×C22⋊Dic13 | C2 | semidirect |
| 4. C2×#88183 | C2 | direct (N × H) |
| 5. C22×#6103 | C2 | semidirect |
| 6. C22×#6101 | C2 | semidirect |
| 11. C23×C4×C13 | C22 | semidirect |
| 16. C2×C22⋊Dic13 | C22 | semidirect |
| 17. #88183 | C22 | direct (N × H) |
| 18. C2×#6103 | C22 | semidirect |
| 19. C2×#6101 | C22 | semidirect |
| 30. C22×C4×C13 | C23 | semidirect |
| 37. C22⋊Dic13 | C23 | semidirect |
| 38. #6103 | C23 | semidirect |
| 39. #6101 | C23 | semidirect |
| 61. C24×C4 | D13 | semidirect |
| 68. C22×C13 | #123 | semidirect |
| 87. C23×C4 | C2×D13 | semidirect |
| 93. C2×C13 | C2×#123 | semidirect |
| 113. C22×C4 | C22×D13 | semidirect |
| 117. C13 | C22×#123 | semidirect |
| 142. C22 | #88183 | direct (N × H) |
| 152. C2 | C2×#88183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C13 | 2 |
| C23×C22⋊D13 | 2 |
| C22×C22⋊Dic13 | 2 |
| C2×#88183 | 2 |
| C22×#6103 | 2 |
| C22×#6101 | 2 |
| C22×#123 | 13 |