Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. #11718888 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 5. #11718744 | C2 | semidirect |
| 6. #11718742 | C2 | semidirect |
| 7. #11718709 | C2 | semidirect |
| 8. #11718704 | C2 | semidirect |
| 9. C4×#6106 | C2 | semidirect |
| 10. #11718681 | C2 | semidirect |
| 11. D4×#1055 | C2 | semidirect |
| 84. Q8×C13 | #41 | semidirect |
| 85. D4×C13 | SD16 | semidirect |
| 107. D4×Q8 | D13 | semidirect |
| 205. C13 | #3298 | semidirect |
| 213. Q8 | #6129 | semidirect |
| 217. D4 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| #11719260 | 2 |
| #11718888 | 2 |
| C2×#88075 | 2 |
| #11718744 | 2 |
| #11718742 | 2 |
| #11718709 | 2 |
| #11718704 | 2 |
| C4×#6106 | 2 |
| #11718681 | 2 |
| D4×#1055 | 2 |
| #3298 | 13 |