Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 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. #11719237 | C2 | semidirect |
| 2. C13×#427 | C2 | semidirect |
| 3. #11718776 | C2 | semidirect |
| 4. C8×C22⋊D13 | C2 | semidirect |
| 5. #11718664 | C2 | semidirect |
| 6. #11718544 | C2 | semidirect |
| 7. #11718541 | C2 | semidirect |
| 8. #11718535 | C2 | semidirect |
| 9. #11718533 | C2 | semidirect |
| 10. #11718531 | C2 | semidirect |
| 11. #11718527 | C2 | semidirect |
| 106. #427 | D13 | semidirect |
| 189. C13 | #3341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719237 | 2 |
| C13×#427 | 2 |
| #11718776 | 2 |
| C8×C22⋊D13 | 2 |
| #11718664 | 2 |
| #11718544 | 2 |
| #11718541 | 2 |
| #11718535 | 2 |
| #11718533 | 2 |
| #11718531 | 2 |
| #11718527 | 2 |
| #3341 | 13 |