Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #11719226 | C2 | semidirect |
| 3. C13×#405 | C2 | semidirect |
| 4. #11718792 | C2 | semidirect |
| 5. #11718767 | C2 | semidirect |
| 6. #11718372 | C2 | semidirect |
| 7. C4×D104 | C2 | semidirect |
| 13. C2×D104 | C4 | semidirect |
| 18. C4×D52 | C22 | semidirect |
| 19. C13×#97 | C22 | semidirect |
| 20. C4×C8×C13 | C22 | semidirect |
| 21. #88061 | C22 | semidirect |
| 22. #88058 | C22 | semidirect |
| 23. #88057 | C22 | semidirect |
| 28. C2×D52 | C2×C4 | semidirect |
| 32. C2×C8×C13 | C2×C4 | semidirect |
| 43. D104 | C2×C4 | semidirect |
| 44. D104 | C2×C4 | semidirect |
| 69. #405 | D13 | semidirect |
| 95. #97 | C2×D13 | semidirect |
| 96. C4×C8 | C2×D13 | semidirect |
| 111. C2×C8 | C4×D13 | semidirect |
| 122. C13 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D104 | 2 |
| #11719226 | 2 |
| C13×#405 | 2 |
| #11718792 | 2 |
| #11718767 | 2 |
| #11718372 | 2 |
| C4×D104 | 2 |
| #2948 | 13 |