Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719256 | C2 | semidirect |
| 2. D4×D52 | C2 | semidirect |
| 3. C4×C13×D8 | C2 | semidirect |
| 4. #11718817 | C2 | semidirect |
| 5. #11718676 | C2 | semidirect |
| 6. #11718668 | C2 | semidirect |
| 7. #11718543 | C2 | semidirect |
| 8. #11718436 | C2 | semidirect |
| 9. D13×#102 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 17. C4×D4×C13 | C22 | semidirect |
| 18. #88192 | C22 | semidirect |
| 19. C2×#6104 | C22 | semidirect |
| 22. C2×C8×D13 | C22 | semidirect |
| 24. C4⋊C4×D13 | C22 | semidirect |
| 29. #88123 | C22 | semidirect |
| 30. C13×#107 | C22 | semidirect |
| 32. C13×#102 | C22 | semidirect |
| 33. C4×C8×C13 | C22 | semidirect |
| 35. #88061 | C22 | semidirect |
| 36. #88061 | C22 | semidirect |
| 37. #88060 | C22 | semidirect |
| 38. #88049 | C22 | semidirect |
| 39. #88047 | C22 | semidirect |
| 40. C4⋊#1055 | C22 | semidirect |
| 89. D4×C13 | #41 | semidirect |
| 106. D52 | D8 | semidirect |
| 122. C4×D8 | D13 | semidirect |
| 163. C4×D4 | C2×D13 | semidirect |
| 166. #107 | C2×D13 | semidirect |
| 173. #102 | C2×D13 | semidirect |
| 175. C4×C8 | C2×D13 | semidirect |
| 220. C13 | #3294 | semidirect |
| 240. D4 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719256 | 2 |
| D4×D52 | 2 |
| C4×C13×D8 | 2 |
| #11718817 | 2 |
| #11718676 | 2 |
| #11718668 | 2 |
| #11718543 | 2 |
| #11718436 | 2 |
| D13×#102 | 2 |
| #11718355 | 2 |
| C8×D52 | 2 |
| #3294 | 13 |