Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11719272 | C2 | semidirect |
| 3. C8×Q8×C13 | C2 | semidirect |
| 4. #11718510 | C2 | semidirect |
| 7. #11718490 | C2 | semidirect |
| 8. C4×Dic52 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 105. C8×Q8 | D13 | semidirect |
| 188. C13 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719289 | 2 |
| #11719272 | 2 |
| C8×Q8×C13 | 2 |
| #11718510 | 2 |
| #11718507 | 2 |
| #11718506 | 2 |
| #11718490 | 2 |
| C4×Dic52 | 2 |
| #11718358 | 2 |
| C4×#6095 | 2 |
| #11718342 | 2 |
| #3364 | 13 |