Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88172 | C2 | semidirect |
| 3. C2×Q16×D13 | C2 | semidirect |
| 4. #11719429 | C2 | semidirect |
| 5. C13×#494 | C2 | semidirect |
| 6. #11718852 | C2 | semidirect |
| 7. #11718851 | C2 | semidirect |
| 8. #11718842 | C2 | semidirect |
| 9. #11718747 | C2 | semidirect |
| 10. #11718357 | C2 | semidirect |
| 11. #11718350 | C2 | semidirect |
| 114. #494 | D13 | semidirect |
| 198. C13 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×#88172 | 2 |
| C2×Q16×D13 | 2 |
| #11719429 | 2 |
| C13×#494 | 2 |
| #11718852 | 2 |
| #11718851 | 2 |
| #11718842 | 2 |
| #11718747 | 2 |
| #11718357 | 2 |
| #11718350 | 2 |
| #3156 | 13 |