Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #11719433 | C2 | semidirect |
| 3. C13×#474 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718680 | C2 | semidirect |
| 6. #11718547 | C2 | semidirect |
| 7. #11718536 | C2 | semidirect |
| 8. #11718502 | C2 | semidirect |
| 9. #11718498 | C2 | semidirect |
| 10. #11718441 | C2 | semidirect |
| 11. #11718423 | C2 | semidirect |
| 120. #474 | D13 | semidirect |
| 224. C13 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| #11719253 | 2 |
| C13×#474 | 2 |
| #11718748 | 2 |
| #11718680 | 2 |
| #11718547 | 2 |
| #11718536 | 2 |
| #11718502 | 2 |
| #11718498 | 2 |
| #11718441 | 2 |
| #11718423 | 2 |
| #3254 | 13 |