Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11719264 | C2 | semidirect |
| 2. C4×C13×D8 | C2 | semidirect |
| 3. #11718816 | C2 | semidirect |
| 5. #11718677 | C2 | semidirect |
| 6. #11718534 | C2 | semidirect |
| 7. #11718533 | C2 | semidirect |
| 8. #11718448 | C2 | semidirect |
| 9. #11718423 | C2 | semidirect |
| 10. #11718357 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 109. C4×D8 | D13 | semidirect |
| 192. C13 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719264 | 2 |
| C4×C13×D8 | 2 |
| #11718816 | 2 |
| #11718812 | 2 |
| #11718677 | 2 |
| #11718534 | 2 |
| #11718533 | 2 |
| #11718448 | 2 |
| #11718423 | 2 |
| #11718357 | 2 |
| C8×Dic26 | 2 |
| #3396 | 13 |