Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. C2×#88205 | C2 | semidirect |
| 3. D4×Dic26 | C2 | semidirect |
| 4. #11718900 | C2 | semidirect |
| 5. #11718737 | C2 | semidirect |
| 6. #11718736 | C2 | semidirect |
| 7. #11718703 | C2 | semidirect |
| 8. #11718701 | C2 | semidirect |
| 9. #11718692 | C2 | semidirect |
| 10. C4×#6107 | C2 | semidirect |
| 11. #11718673 | C2 | semidirect |
| 68. #6107 | D4 | semidirect |
| 137. C4×C13 | #137 | semidirect |
| 218. C13 | #3278 | semidirect |
| 265. C4 | #88205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| C2×#88205 | 2 |
| D4×Dic26 | 2 |
| #11718900 | 2 |
| #11718737 | 2 |
| #11718736 | 2 |
| #11718703 | 2 |
| #11718701 | 2 |
| #11718692 | 2 |
| C4×#6107 | 2 |
| #11718673 | 2 |
| #3278 | 13 |