Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D13 | C2 | semidirect |
| 3. C13×#460 | C2 | semidirect |
| 4. #11718831 | C2 | semidirect |
| 5. #11718825 | C2 | semidirect |
| 6. #11718736 | C2 | semidirect |
| 7. #11718682 | C2 | semidirect |
| 8. #11718511 | C2 | semidirect |
| 9. #11718496 | C2 | semidirect |
| 10. #11718435 | C2 | semidirect |
| 11. #11718418 | C2 | semidirect |
| 87. Q8×C13 | #41 | semidirect |
| 114. Dic26 | #41 | semidirect |
| 123. #460 | D13 | semidirect |
| 223. C13 | #3112 | semidirect |
| 231. Q8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| C4×Q8×D13 | 2 |
| C13×#460 | 2 |
| #11718831 | 2 |
| #11718825 | 2 |
| #11718736 | 2 |
| #11718682 | 2 |
| #11718511 | 2 |
| #11718496 | 2 |
| #11718435 | 2 |
| #11718418 | 2 |
| #3112 | 13 |