Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×C4×D4×C13 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C2×#88128 | C2 | semidirect |
| 4. #11718676 | C2 | direct (N × H) |
| 5. C2×#88049 | C2 | semidirect |
| 6. C2×C4⋊#1055 | C2 | semidirect |
| 13. C4×D4×C13 | C22 | semidirect |
| 18. C2×#6104 | C22 | semidirect |
| 21. #88128 | C22 | semidirect |
| 22. #88049 | C22 | semidirect |
| 23. C4⋊#1055 | C22 | semidirect |
| 28. C2×D4×C13 | D4 | semidirect |
| 64. D4×C13 | C2×D4 | semidirect |
| 69. C2×C4×C13 | D8 | semidirect |
| 84. C2×C4×D4 | D13 | semidirect |
| 103. C4×C13 | C2×D8 | semidirect |
| 117. C4×D4 | C2×D13 | semidirect |
| 124. C2×C13 | #459 | semidirect |
| 141. C2×D4 | D52 | semidirect |
| 157. C13 | C2×#459 | semidirect |
| 174. D4 | C2×D52 | semidirect |
| 179. C2×C4 | #6104 | semidirect |
| 202. C4 | C2×#6104 | semidirect |
| 207. C2 | #11718676 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C22×#6104 | 2 |
| C2×#88128 | 2 |
| #11718676 | 2 |
| C2×#88049 | 2 |
| C2×C4⋊#1055 | 2 |
| C2×#459 | 13 |