Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #11719089 | C2 | semidirect |
| 5. #11718266 | C2 | semidirect |
| 9. C2×C13×M16 | C4 | semidirect |
| 10. C22×#1055 | C4 | semidirect |
| 13. C2×#6094 | C4 | semidirect |
| 15. C2×C8×D13 | C4 | semidirect |
| 17. #88121 | C4 | semidirect |
| 19. #88113 | C4 | semidirect |
| 100. C2×M16 | #261 | semidirect |
| 144. C13 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| #11719132 | 2 |
| #11719116 | 2 |
| #11719089 | 2 |
| #11718266 | 2 |
| #1757 | 13 |