Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 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. #11719427 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 6. #11718516 | C2 | semidirect |
| 7. #11718515 | C2 | semidirect |
| 8. #11718512 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 58. #6105 | Q8 | semidirect |
| 94. Dic26 | SD16 | semidirect |
| 95. Dic26 | C2×Q8 | semidirect |
| 98. #1055 | C2×Q8 | semidirect |
| 190. C13 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719427 | 2 |
| D4×Dic26 | 2 |
| C13×#476 | 2 |
| #11718740 | 2 |
| C4×#6105 | 2 |
| #11718516 | 2 |
| #11718515 | 2 |
| #11718512 | 2 |
| #11718491 | 2 |
| #11718422 | 2 |
| #11718419 | 2 |
| Q8×SD16 | 13 |