Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
616 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×C8×C13 | C2 | semidirect |
| 2. C2×#88184 | C2 | semidirect |
| 3. C22×D104 | C2 | semidirect |
| 4. #11718776 | C2 | direct (N × H) |
| 5. C2×#88061 | C2 | semidirect |
| 6. C2×#88058 | C2 | semidirect |
| 13. C22×C8×C13 | C22 | semidirect |
| 15. #88184 | C22 | semidirect |
| 19. C2×D104 | C22 | semidirect |
| 20. #88061 | C22 | semidirect |
| 21. #88058 | C22 | semidirect |
| 39. C2×C8×C13 | D4 | semidirect |
| 49. C23×C13 | D8 | semidirect |
| 72. C8×C13 | C2×D4 | semidirect |
| 74. C23×C8 | D13 | semidirect |
| 84. C22×C13 | C2×D8 | semidirect |
| 104. C22×C8 | C2×D13 | semidirect |
| 112. C2×C13 | #466 | semidirect |
| 135. C2×C8 | C22⋊D13 | semidirect |
| 141. C13 | C2×#466 | semidirect |
| 148. C23 | D104 | semidirect |
| 167. C8 | C2×C22⋊D13 | semidirect |
| 176. C22 | C2×D104 | semidirect |
| 187. C2 | #11718776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C13 | 2 |
| C2×#88184 | 2 |
| C22×D104 | 2 |
| #11718776 | 2 |
| C2×#88061 | 2 |
| C2×#88058 | 2 |
| C2×#466 | 13 |