Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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. Q8×#1055 | C2 | semidirect |
| 3. #11718673 | C2 | semidirect |
| 4. #11718587 | C2 | semidirect |
| 5. C4×#6099 | C2 | semidirect |
| 37. Q8×C13 | M16 | semidirect |
| 49. #1055 | #41 | semidirect |
| 98. C13 | #2971 | semidirect |
| 100. Q8 | #6099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#41 | 2 |
| Q8×#1055 | 2 |
| #11718673 | 2 |
| #11718587 | 2 |
| C4×#6099 | 2 |
| #2971 | 13 |