Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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. D4×Q8×C13 | C2 | semidirect |
| 2. #11719290 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 4. #11718750 | C2 | semidirect |
| 5. #11718749 | C2 | semidirect |
| 6. #11718745 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 8. C4×#6105 | C2 | semidirect |
| 9. #11718677 | C2 | semidirect |
| 11. #11718675 | C2 | semidirect |
| 104. D4×Q8 | D13 | semidirect |
| 198. C13 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| #11719290 | 2 |
| #11718755 | 2 |
| #11718750 | 2 |
| #11718749 | 2 |
| #11718745 | 2 |
| #11718685 | 2 |
| C4×#6105 | 2 |
| #11718677 | 2 |
| #11718676 | 2 |
| #11718675 | 2 |
| #3373 | 13 |