Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×Q16×D13 | C2 | semidirect |
| 3. #11719281 | C2 | semidirect |
| 4. C4×C13×Q16 | C2 | semidirect |
| 5. #11718689 | C2 | semidirect |
| 6. #11718548 | C2 | semidirect |
| 7. #11718544 | C2 | semidirect |
| 8. #11718471 | C2 | semidirect |
| 9. #11718467 | C2 | semidirect |
| 10. #11718357 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 56. C13×Q16 | D4 | semidirect |
| 121. C4×Q16 | D13 | semidirect |
| 132. C2×D13 | #135 | semidirect |
| 194. Q16 | D52 | semidirect |
| 216. C13 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×Q16×D13 | 2 |
| #11719281 | 2 |
| C4×C13×Q16 | 2 |
| #11718689 | 2 |
| #11718548 | 2 |
| #11718544 | 2 |
| #11718471 | 2 |
| #11718467 | 2 |
| #11718357 | 2 |
| C8×D52 | 2 |
| #3285 | 13 |