Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 1. #11719395 | C2 | semidirect |
| 2. C13×#499 | C2 | semidirect |
| 3. #11718727 | C2 | semidirect |
| 4. #11718539 | C2 | semidirect |
| 5. #11718535 | C2 | semidirect |
| 8. #11718532 | C2 | semidirect |
| 9. #11718531 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 66. D104 | Q8 | semidirect |
| 93. #499 | D13 | semidirect |
| 175. C13 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719395 | 2 |
| C13×#499 | 2 |
| #11718727 | 2 |
| #11718539 | 2 |
| #11718535 | 2 |
| #11718533 | 2 |
| #11718532 | 2 |
| #11718531 | 2 |
| C4×D104 | 2 |
| C8×Dic26 | 2 |
| #3380 | 13 |