Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #11719272 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718741 | C2 | semidirect |
| 6. #11718739 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 60. #6105 | Q8 | semidirect |
| 94. Dic26 | C2×Q8 | semidirect |
| 97. #1055 | C2×Q8 | semidirect |
| 189. C13 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| #11719272 | 2 |
| #11718755 | 2 |
| #11718752 | 2 |
| #11718741 | 2 |
| #11718739 | 2 |
| #11718685 | 2 |
| #11718679 | 2 |
| C4×#6105 | 2 |
| #11718670 | 2 |
| #11718668 | 2 |
| #3386 | 13 |