Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D52 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718831 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 6. #11718680 | C2 | semidirect |
| 7. #11718523 | C2 | semidirect |
| 8. D13×#103 | C2 | semidirect |
| 9. #11718439 | C2 | semidirect |
| 10. C8×D52 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 81. Q8×C13 | #41 | semidirect |
| 95. D52 | SD16 | semidirect |
| 115. C4×SD16 | D13 | semidirect |
| 205. C13 | #3298 | semidirect |
| 213. Q8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| #11719256 | 2 |
| C4×C13×SD16 | 2 |
| #11718831 | 2 |
| #11718681 | 2 |
| #11718680 | 2 |
| #11718523 | 2 |
| D13×#103 | 2 |
| #11718439 | 2 |
| C8×D52 | 2 |
| #11718342 | 2 |
| #3298 | 13 |