Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. #11719082 | C2 | semidirect |
| 5. C4×C4⋊#261 | C2 | semidirect |
| 6. #11719057 | C2 | semidirect |
| 7. C42×#261 | C2 | semidirect |
| 14. C13×#117 | C4 | semidirect |
| 15. #88180 | C4 | semidirect |
| 16. #88146 | C4 | semidirect |
| 19. #88131 | C4 | semidirect |
| 20. #88126 | C4 | semidirect |
| 21. #88126 | C4 | semidirect |
| 117. #117 | #261 | semidirect |
| 166. C13 | #2298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#117 | 2 |
| C4×C22⋊#261 | 2 |
| #11719082 | 2 |
| #11719071 | 2 |
| C4×C4⋊#261 | 2 |
| #11719057 | 2 |
| C42×#261 | 2 |
| #2298 | 13 |