Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×#88106 | C2 | semidirect |
| 3. D13⋊M32 | C2 | direct (N × H) |
| 4. C2×#88098 | C2 | semidirect |
| 5. C2×D13⋊C16 | C2 | semidirect |
| 15. #88106 | C22 | semidirect |
| 16. C2×#6092 | C22 | semidirect |
| 17. #88098 | C22 | semidirect |
| 18. D13⋊C16 | C22 | semidirect |
| 41. #6092 | C23 | semidirect |
| 76. C2×D13 | M32 | semidirect |
| 98. C2×C13 | C2×M32 | semidirect |
| 101. D13 | C2×M32 | semidirect |
| 125. C13 | C22×M32 | semidirect |
| 165. C2 | D13⋊M32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D13 | 2 |
| C2×#88106 | 2 |
| D13⋊M32 | 2 |
| C2×#88098 | 2 |
| C2×D13⋊C16 | 2 |
| C22×M32 | 13 |