Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 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. C2×Q8×Dic13 | C2 | semidirect |
| 4. #11718891 | C2 | semidirect |
| 6. #11718612 | C2 | semidirect |
| 7. C22⋊C4×Dic13 | C2 | semidirect |
| 8. #11718597 | C2 | semidirect |
| 9. C42×Dic13 | C2 | semidirect |
| 13. C13×#124 | C4 | semidirect |
| 33. C2×Q8×C13 | C2×C4 | semidirect |
| 47. C13×C22⋊C4 | C2×C4 | semidirect |
| 48. C42×C13 | C2×C4 | semidirect |
| 115. Dic13 | #124 | direct (N × H) |
| 119. #124 | Dic13 | direct (N × H) |
| 145. C2×Q8 | C2×Dic13 | semidirect |
| 164. C22⋊C4 | C2×Dic13 | semidirect |
| 170. C42 | C2×Dic13 | semidirect |
| 171. C13 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| C2×Q8×Dic13 | 2 |
| C2×D4×Dic13 | 2 |
| #11718891 | 2 |
| #11718882 | 2 |
| #11718612 | 2 |
| C22⋊C4×Dic13 | 2 |
| #11718597 | 2 |
| C42×Dic13 | 2 |
| C4×#124 | 13 |