Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#88240 | C2 | semidirect |
| 3. C2×#88118 | C2 | semidirect |
| 4. #11719147 | C2 | semidirect |
| 5. C2×#88116 | C2 | semidirect |
| 6. #11718268 | C2 | semidirect |
| 7. (C2×#261)⋊C8 | C2 | semidirect |
| 18. C2×C13×SD16 | C4 | semidirect |
| 19. C2×#6107 | C4 | semidirect |
| 20. C2×#6104 | C4 | semidirect |
| 23. C2×#6095 | C4 | semidirect |
| 137. C2×SD16 | #261 | semidirect |
| 199. C13 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88240 | 2 |
| C2×#88170 | 2 |
| C2×#88118 | 2 |
| #11719147 | 2 |
| C2×#88116 | 2 |
| #11718268 | 2 |
| (C2×#261)⋊C8 | 2 |
| #1876 | 13 |