Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×C13×D8 | C2 | semidirect |
| 3. C4×D104 | C2 | semidirect |
| 4. #11718154 | C2 | semidirect |
| 5. #11718083 | C2 | semidirect |
| 6. #11718081 | C2 | semidirect |
| 7. C4×#6090 | C2 | semidirect |
| 15. #88066 | C4 | direct (N × H) |
| 25. C13×D8 | C2×C4 | semidirect |
| 34. D104 | C2×C4 | semidirect |
| 36. #6090 | C2×C4 | semidirect |
| 56. C4×D8 | D13 | semidirect |
| 70. C4×C13 | D16 | semidirect |
| 98. D8 | C4×D13 | semidirect |
| 108. C13 | C4×D16 | semidirect |
| 135. C4 | #88066 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×D8 | 2 |
| C2×#88066 | 2 |
| C4×D104 | 2 |
| #11718154 | 2 |
| #11718083 | 2 |
| #11718081 | 2 |
| C4×#6090 | 2 |
| C4×D16 | 13 |