Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719430 | C2 | semidirect |
| 2. C4×#6131 | C2 | semidirect |
| 3. C13×#477 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718546 | C2 | semidirect |
| 7. #11718533 | C2 | semidirect |
| 8. #11718504 | C2 | semidirect |
| 9. #11718494 | C2 | semidirect |
| 10. #11718472 | C2 | semidirect |
| 11. #11718449 | C2 | semidirect |
| 89. Q8×C13 | #41 | semidirect |
| 107. D52 | #41 | semidirect |
| 121. #477 | D13 | semidirect |
| 227. C13 | #3106 | semidirect |
| 233. Q8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719430 | 2 |
| C4×#6131 | 2 |
| C13×#477 | 2 |
| #11718745 | 2 |
| #11718688 | 2 |
| #11718546 | 2 |
| #11718533 | 2 |
| #11718504 | 2 |
| #11718494 | 2 |
| #11718472 | 2 |
| #11718449 | 2 |
| #3106 | 13 |