Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719247 | C2 | semidirect |
| 3. C8×D4×C13 | C2 | semidirect |
| 4. #11718775 | C2 | semidirect |
| 5. #11718767 | C2 | semidirect |
| 6. #11718511 | C2 | semidirect |
| 7. #11718507 | C2 | semidirect |
| 8. #11718398 | C2 | semidirect |
| 9. #11718384 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. #11718341 | C2 | semidirect |
| 108. C8×D4 | D13 | semidirect |
| 193. C13 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719268 | 2 |
| #11719247 | 2 |
| C8×D4×C13 | 2 |
| #11718775 | 2 |
| #11718767 | 2 |
| #11718511 | 2 |
| #11718507 | 2 |
| #11718398 | 2 |
| #11718384 | 2 |
| C4×#6095 | 2 |
| #11718341 | 2 |
| #3340 | 13 |