Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719284 | C2 | semidirect |
| 3. C4×C13×Q16 | C2 | semidirect |
| 4. #11718848 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718682 | C2 | semidirect |
| 7. #11718543 | C2 | semidirect |
| 8. #11718473 | C2 | semidirect |
| 9. #11718464 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. #11718349 | C2 | semidirect |
| 115. C4×Q16 | D13 | semidirect |
| 204. C13 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| #11719282 | 2 |
| C4×C13×Q16 | 2 |
| #11718848 | 2 |
| #11718688 | 2 |
| #11718682 | 2 |
| #11718543 | 2 |
| #11718473 | 2 |
| #11718464 | 2 |
| #11718355 | 2 |
| #11718349 | 2 |
| #3333 | 13 |