Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#88237 | C2 | semidirect |
| 3. #11719156 | C2 | direct (N × H) |
| 4. C2×#88107 | C2 | semidirect |
| 5. C22×Q8×C13 | C4 | semidirect |
| 9. C2×#6131 | C4 | semidirect |
| 11. C22×D52 | C4 | semidirect |
| 13. C22×C4×D13 | C4 | semidirect |
| 17. #88237 | C22 | semidirect |
| 20. #88107 | C22 | semidirect |
| 26. C2×Q8×C13 | C2×C4 | semidirect |
| 39. C2×D52 | C2×C4 | semidirect |
| 45. C2×C4×D13 | C2×C4 | semidirect |
| 115. C22×Q8 | #261 | semidirect |
| 128. C2×C13 | #410 | semidirect |
| 141. C2×Q8 | C2×#261 | semidirect |
| 166. C13 | C2×#410 | semidirect |
| 223. C2 | #11719156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C2×#88237 | 2 |
| #11719156 | 2 |
| C2×#88107 | 2 |
| C2×#410 | 13 |