Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #11719275 | C2 | semidirect |
| 3. C8×Q8×C13 | C2 | semidirect |
| 4. #11718512 | C2 | semidirect |
| 7. #11718342 | C2 | semidirect |
| 45. Q8×C13 | SD16 | semidirect |
| 65. C8×Q8 | D13 | semidirect |
| 117. C13 | #3359 | semidirect |
| 122. Q8 | #6095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| #11719275 | 2 |
| C8×Q8×C13 | 2 |
| #11718512 | 2 |
| #11718502 | 2 |
| C4×#6095 | 2 |
| #11718342 | 2 |
| #3359 | 13 |