Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #11719082 | C2 | semidirect |
| 3. C4⋊C4×#261 | C2 | semidirect |
| 6. #11719061 | C2 | semidirect |
| 7. C42×#261 | C2 | semidirect |
| 14. C13×#126 | C4 | semidirect |
| 15. #88152 | C4 | semidirect |
| 18. #88133 | C4 | semidirect |
| 19. #88130 | C4 | semidirect |
| 38. C13×C4⋊C4 | C2×C4 | semidirect |
| 40. C42×C13 | C2×C4 | semidirect |
| 44. C4⋊Dic13 | C2×C4 | semidirect |
| 45. #6101 | C2×C4 | semidirect |
| 46. #6101 | C2×C4 | semidirect |
| 47. C4×Dic13 | C2×C4 | semidirect |
| 88. #261 | #126 | direct (N × H) |
| 97. #126 | #261 | direct (N × H) |
| 127. C4⋊C4 | C2×#261 | semidirect |
| 137. C42 | C2×#261 | semidirect |
| 138. C13 | C4×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#126 | 2 |
| #11719082 | 2 |
| C4⋊C4×#261 | 2 |
| #11719071 | 2 |
| C22⋊C4×#261 | 2 |
| #11719061 | 2 |
| C42×#261 | 2 |
| C4×#126 | 13 |