Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 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 |
| 3. C2×#88178 | C2 | semidirect |
| 4. C22×#6095 | C2 | semidirect |
| 5. #11718775 | C2 | direct (N × H) |
| 6. C2×#88061 | C2 | semidirect |
| 7. C2×#88057 | C2 | semidirect |
| 8. C2×#88056 | C2 | semidirect |
| 16. C22×C8×C13 | C22 | semidirect |
| 24. #88178 | C22 | semidirect |
| 27. C2×#6095 | C22 | semidirect |
| 28. #88061 | C22 | semidirect |
| 29. #88057 | C22 | semidirect |
| 30. #88056 | C22 | semidirect |
| 54. C2×C8×C13 | D4 | semidirect |
| 68. C23×C13 | SD16 | semidirect |
| 98. C8×C13 | C2×D4 | semidirect |
| 100. C23×C8 | D13 | semidirect |
| 112. C22×C13 | C2×SD16 | semidirect |
| 135. C22×C8 | C2×D13 | semidirect |
| 149. C2×C13 | #465 | semidirect |
| 178. C2×C8 | C22⋊D13 | semidirect |
| 188. C13 | C2×#465 | semidirect |
| 195. C23 | #6095 | semidirect |
| 221. C8 | C2×C22⋊D13 | semidirect |
| 230. C22 | C2×#6095 | semidirect |
| 243. C2 | #11718775 | 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 |
| C2×#88178 | 2 |
| C22×#6095 | 2 |
| #11718775 | 2 |
| C2×#88061 | 2 |
| C2×#88057 | 2 |
| C2×#88056 | 2 |
| C2×#465 | 13 |