Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#88251 | C2 | semidirect |
| 2. C2×C13×#127 | C2 | semidirect |
| 3. C2×#88186 | C2 | semidirect |
| 4. C2×#88073 | C2 | semidirect |
| 5. #11718738 | C2 | direct (N × H) |
| 6. C2×#88045 | C2 | semidirect |
| 9. C22×D4×C13 | C22 | semidirect |
| 13. #88251 | C22 | semidirect |
| 18. C13×#127 | C22 | semidirect |
| 19. C2×C42×C13 | C22 | semidirect |
| 22. #88186 | C22 | semidirect |
| 24. C2×#6099 | C22 | semidirect |
| 25. #88073 | C22 | semidirect |
| 26. #88045 | C22 | semidirect |
| 39. C2×D4×C13 | C23 | semidirect |
| 53. #6127 | D4 | semidirect |
| 55. C2×D52 | D4 | semidirect |
| 57. C2×Dic26 | D4 | semidirect |
| 59. C42×C13 | C23 | semidirect |
| 63. #6099 | C23 | semidirect |
| 95. D52 | C2×D4 | semidirect |
| 99. Dic26 | C2×D4 | semidirect |
| 103. C2×#127 | D13 | semidirect |
| 135. C22×D4 | C2×D13 | semidirect |
| 142. #127 | C2×D13 | semidirect |
| 143. C2×C42 | C2×D13 | semidirect |
| 150. C2×C13 | #453 | semidirect |
| 179. C2×D4 | C22×D13 | semidirect |
| 190. C42 | C22×D13 | semidirect |
| 191. C13 | C2×#453 | semidirect |
| 251. C2 | #11718738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88251 | 2 |
| C2×C13×#127 | 2 |
| C2×#88186 | 2 |
| C2×#88073 | 2 |
| #11718738 | 2 |
| C2×#88045 | 2 |
| C2×#453 | 13 |