Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#88147 | C2 | semidirect |
| 3. C2×C13×#106 | C2 | semidirect |
| 4. C2×#88055 | C2 | semidirect |
| 5. C2×#88049 | C2 | semidirect |
| 6. #11718530 | C2 | direct (N × H) |
| 14. C2×D104 | C4 | semidirect |
| 17. #88147 | C22 | semidirect |
| 18. C13×#106 | C22 | semidirect |
| 19. #88055 | C22 | semidirect |
| 20. #88049 | C22 | semidirect |
| 27. C2×D52 | C2×C4 | semidirect |
| 31. C2×C8×C13 | C2×C4 | semidirect |
| 40. D104 | C2×C4 | semidirect |
| 57. D52 | C22×C4 | semidirect |
| 59. C8×C13 | C22×C4 | semidirect |
| 64. C2×#106 | D13 | semidirect |
| 90. #106 | C2×D13 | semidirect |
| 93. C2×C13 | #442 | semidirect |
| 110. C2×C8 | C4×D13 | semidirect |
| 117. C13 | C2×#442 | semidirect |
| 136. C8 | C2×C4×D13 | semidirect |
| 150. C2 | #11718530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D104 | 2 |
| C2×#88147 | 2 |
| C2×C13×#106 | 2 |
| C2×#88055 | 2 |
| C2×#88049 | 2 |
| #11718530 | 2 |
| C2×#442 | 13 |