Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11719171 | C2 | semidirect |
| 3. #11719151 | C2 | semidirect |
| 4. #11719150 | C2 | semidirect |
| 5. #11719071 | C2 | semidirect |
| 7. C23×#261 | C22 | semidirect |
| 11. C2×C22⋊#261 | C22 | semidirect |
| 12. C2×C4⋊#261 | C22 | semidirect |
| 13. C2×C4×#261 | C22 | semidirect |
| 14. C13×#120 | C4 | semidirect |
| 15. #88207 | C4 | semidirect |
| 16. #88191 | C4 | semidirect |
| 17. #88136 | C4 | semidirect |
| 19. (C2×#261)⋊C4 | C22 | semidirect |
| 20. C24×C13 | C2×C4 | semidirect |
| 23. C23×D13 | C2×C4 | semidirect |
| 41. C13×C22⋊C4 | C2×C4 | semidirect |
| 42. C22⋊Dic13 | C2×C4 | semidirect |
| 43. #6103 | C2×C4 | semidirect |
| 105. #120 | #261 | semidirect |
| 125. C24 | C2×#261 | semidirect |
| 142. C22⋊C4 | C2×#261 | semidirect |
| 144. C13 | #2375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#120 | 2 |
| #11719171 | 2 |
| #11719151 | 2 |
| #11719150 | 2 |
| #11719071 | 2 |
| #2375 | 13 |