Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#88173 | C2 | semidirect |
| 2. #11719282 | C2 | semidirect |
| 3. C4×C13×Q16 | C2 | semidirect |
| 4. #11718688 | C2 | semidirect |
| 5. #11718544 | C2 | semidirect |
| 6. #11718472 | C2 | semidirect |
| 7. #11718356 | C2 | semidirect |
| 8. C8×D52 | C2 | semidirect |
| 40. C13×Q16 | D4 | semidirect |
| 85. C4×Q16 | D13 | semidirect |
| 97. C4×C13 | #135 | semidirect |
| 137. Q16 | D52 | semidirect |
| 152. C13 | #3287 | semidirect |
| 187. C4 | #88173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| #11719282 | 2 |
| C4×C13×Q16 | 2 |
| #11718688 | 2 |
| #11718544 | 2 |
| #11718472 | 2 |
| #11718356 | 2 |
| C8×D52 | 2 |
| #3287 | 13 |