Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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. C2×#88100 | C2 | direct (N × H) |
| 7. C22×#1057 | C4 | semidirect |
| 10. C2×D13⋊C8 | C4 | semidirect |
| 12. C22×C8×C13 | C4 | semidirect |
| 13. C22×#1055 | C4 | semidirect |
| 14. C2×C8×D13 | C4 | semidirect |
| 16. #88100 | C22 | direct (N × H) |
| 26. C2×#1057 | C2×C4 | semidirect |
| 29. D13⋊C8 | C2×C4 | semidirect |
| 31. C2×C8×C13 | C2×C4 | semidirect |
| 32. C2×#1055 | C2×C4 | semidirect |
| 33. C8×D13 | C2×C4 | semidirect |
| 51. #1057 | C22×C4 | semidirect |
| 52. C8×C13 | C22×C4 | semidirect |
| 53. #1055 | C22×C4 | semidirect |
| 58. C22×C13 | #97 | semidirect |
| 60. C2×D13 | #97 | semidirect |
| 77. C22×C8 | #261 | semidirect |
| 81. C2×C13 | C2×#97 | semidirect |
| 83. D13 | C2×#97 | semidirect |
| 100. C2×C8 | C2×#261 | semidirect |
| 103. C13 | C22×#97 | semidirect |
| 121. C8 | C22×#261 | semidirect |
| 126. C22 | #88100 | direct (N × H) |
| 135. C2 | C2×#88100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#261 | 2 |
| C22×D13⋊C8 | 2 |
| C22×C8×D13 | 2 |
| C2×#88100 | 2 |
| C22×#97 | 13 |