Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #11719290 | C2 | semidirect |
| 2. #11719289 | C2 | semidirect |
| 3. C8×Q8×C13 | C2 | semidirect |
| 4. #11718510 | C2 | semidirect |
| 5. #11718506 | C2 | semidirect |
| 6. #11718505 | C2 | semidirect |
| 8. #11718357 | C2 | semidirect |
| 9. #11718354 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 112. C8×Q8 | D13 | semidirect |
| 201. C13 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719289 | 2 |
| C8×Q8×C13 | 2 |
| #11718510 | 2 |
| #11718506 | 2 |
| #11718505 | 2 |
| #11718504 | 2 |
| #11718357 | 2 |
| #11718354 | 2 |
| C4×#6095 | 2 |
| #3394 | 13 |