Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#88169 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 4. C4×C13×SD16 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 6. #11718680 | C2 | semidirect |
| 7. #11718529 | C2 | semidirect |
| 8. #11718469 | C2 | semidirect |
| 9. #11718444 | C2 | semidirect |
| 10. #11718360 | C2 | semidirect |
| 11. #11718349 | C2 | semidirect |
| 57. C13×SD16 | D4 | semidirect |
| 122. C4×SD16 | D13 | semidirect |
| 135. C4×C13 | #137 | semidirect |
| 195. SD16 | D52 | semidirect |
| 216. C13 | #3276 | semidirect |
| 261. C4 | #88169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88169 | 2 |
| Q8×D52 | 2 |
| #11719260 | 2 |
| C4×C13×SD16 | 2 |
| #11718692 | 2 |
| #11718680 | 2 |
| #11718529 | 2 |
| #11718469 | 2 |
| #11718444 | 2 |
| #11718360 | 2 |
| #11718349 | 2 |
| #3276 | 13 |