Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 4. #11719083 | C2 | semidirect |
| 6. C4×C4⋊#261 | C2 | semidirect |
| 17. C13×#117 | C4 | semidirect |
| 18. #88180 | C4 | semidirect |
| 19. #88146 | C4 | semidirect |
| 22. #88131 | C4 | semidirect |
| 23. #88126 | C4 | semidirect |
| 46. C13×C4⋊C4 | C2×C4 | semidirect |
| 48. C42×C13 | C2×C4 | semidirect |
| 51. C4⋊Dic13 | C2×C4 | semidirect |
| 52. #6101 | C2×C4 | semidirect |
| 53. C4×Dic13 | C2×C4 | semidirect |
| 54. C4×Dic13 | C2×C4 | semidirect |
| 68. C2×C4×C13 | C4⋊C4 | semidirect |
| 72. C2×Dic13 | C4⋊C4 | semidirect |
| 77. C4×D13 | C4⋊C4 | semidirect |
| 78. C4×D13 | C4⋊C4 | semidirect |
| 114. #117 | #261 | semidirect |
| 150. C4⋊C4 | C2×#261 | semidirect |
| 160. C42 | C2×#261 | semidirect |
| 161. C13 | #2296 | semidirect |
| 185. C2×C4 | C4⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88237 | 2 |
| C22×C4×#261 | 2 |
| D13×#117 | 2 |
| #11719083 | 2 |
| #11719070 | 2 |
| C4×C4⋊#261 | 2 |
| #2296 | 13 |