Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11719182 | C2 | semidirect |
| 2. C4×#6127 | C2 | semidirect |
| 3. C13×#431 | C2 | semidirect |
| 4. #11718511 | C2 | semidirect |
| 5. #11718509 | C2 | semidirect |
| 6. #11718504 | C2 | semidirect |
| 7. #11718503 | C2 | semidirect |
| 8. #11718398 | C2 | semidirect |
| 9. #11718395 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 108. D52 | #41 | semidirect |
| 115. Dic26 | #41 | semidirect |
| 128. #431 | D13 | semidirect |
| 227. C13 | #3106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719182 | 2 |
| C4×#6127 | 2 |
| C13×#431 | 2 |
| #11718511 | 2 |
| #11718509 | 2 |
| #11718504 | 2 |
| #11718503 | 2 |
| #11718398 | 2 |
| #11718395 | 2 |
| C4×D104 | 2 |
| C4×#6095 | 2 |
| #3106 | 13 |