Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719248 | C2 | semidirect |
| 2. D4×Dic26 | C2 | semidirect |
| 5. #11718669 | C2 | semidirect |
| 6. #11718668 | C2 | semidirect |
| 7. #11718537 | C2 | semidirect |
| 8. #11718424 | C2 | semidirect |
| 9. #11718422 | C2 | semidirect |
| 10. #11718341 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 52. C13×D8 | Q8 | semidirect |
| 79. D4×C13 | C2×Q8 | semidirect |
| 98. C8×C13 | C2×Q8 | semidirect |
| 173. D8 | Dic26 | semidirect |
| 194. C13 | #3384 | semidirect |
| 204. D4 | C2×Dic26 | semidirect |
| 220. C8 | C2×Dic26 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719248 | 2 |
| D4×Dic26 | 2 |
| C4×C13×D8 | 2 |
| #11718813 | 2 |
| #11718669 | 2 |
| #11718668 | 2 |
| #11718537 | 2 |
| #11718424 | 2 |
| #11718422 | 2 |
| #11718341 | 2 |
| #11718340 | 2 |
| #3384 | 13 |