Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#88238 | C2 | semidirect |
| 3. C2×#88116 | C2 | semidirect |
| 4. #11719103 | C2 | direct (N × H) |
| 5. C2×#88104 | C2 | semidirect |
| 6. C2×C8×#261 | C2 | semidirect |
| 11. #88238 | C22 | semidirect |
| 15. C2×C13×D8 | C4 | semidirect |
| 16. C2×#6105 | C4 | semidirect |
| 17. #88166 | C4 | semidirect |
| 19. C2×Dic52 | C4 | semidirect |
| 21. #88116 | C22 | semidirect |
| 22. #88104 | C22 | semidirect |
| 23. C8×#261 | C22 | semidirect |
| 45. C13×D8 | C2×C4 | semidirect |
| 47. #6105 | C2×C4 | semidirect |
| 49. Dic52 | C2×C4 | semidirect |
| 100. C2×D8 | #261 | semidirect |
| 113. C2×C13 | #443 | semidirect |
| 129. D8 | C2×#261 | semidirect |
| 145. C13 | C2×#443 | semidirect |
| 185. C2 | #11719103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88238 | 2 |
| C2×#88166 | 2 |
| C2×#88116 | 2 |
| #11719103 | 2 |
| C2×#88104 | 2 |
| C2×C8×#261 | 2 |
| C2×#443 | 13 |