Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 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. C8×Q8×C13 | C2 | semidirect |
| 3. Q8×#1055 | C2 | semidirect |
| 5. #11718492 | C2 | semidirect |
| 7. #11718340 | C2 | semidirect |
| 42. #6094 | Q8 | direct (N × H) |
| 45. Q8×C13 | M16 | semidirect |
| 58. C8×C13 | C2×Q8 | semidirect |
| 60. #1055 | C2×Q8 | semidirect |
| 65. C8×Q8 | D13 | semidirect |
| 118. C13 | Q8×M16 | semidirect |
| 121. Q8 | #6094 | direct (N × H) |
| 135. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D13 | 2 |
| C8×Q8×C13 | 2 |
| Q8×#1055 | 2 |
| #11718498 | 2 |
| #11718492 | 2 |
| C4×#6094 | 2 |
| #11718340 | 2 |
| Q8×M16 | 13 |