Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 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. #11719423 | C2 | semidirect |
| 2. #11719247 | C2 | semidirect |
| 3. C13×#459 | C2 | semidirect |
| 4. #11718815 | C2 | semidirect |
| 5. #11718814 | C2 | semidirect |
| 6. #11718737 | C2 | semidirect |
| 7. C4×#6104 | C2 | semidirect |
| 8. #11718502 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 10. #11718423 | C2 | semidirect |
| 11. #11718418 | C2 | semidirect |
| 107. #1055 | #41 | semidirect |
| 115. #459 | D13 | semidirect |
| 209. C13 | #3397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719423 | 2 |
| #11719247 | 2 |
| C13×#459 | 2 |
| #11718815 | 2 |
| #11718814 | 2 |
| #11718737 | 2 |
| C4×#6104 | 2 |
| #11718502 | 2 |
| #11718492 | 2 |
| #11718423 | 2 |
| #11718418 | 2 |
| #3397 | 13 |