Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
| 4. #11718499 | C2 | semidirect |
| 5. #11718496 | C2 | semidirect |
| 6. #11718349 | C2 | semidirect |
| 7. C4×#6094 | C2 | semidirect |
| 45. Q8×C13 | M16 | semidirect |
| 58. C8×C13 | #41 | semidirect |
| 60. #1055 | #41 | semidirect |
| 63. C8×Q8 | D13 | semidirect |
| 118. C13 | #2971 | semidirect |
| 120. Q8 | #6094 | semidirect |
| 135. C8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6131 | 2 |
| C8×Q8×C13 | 2 |
| Q8×#1055 | 2 |
| #11718499 | 2 |
| #11718496 | 2 |
| #11718349 | 2 |
| C4×#6094 | 2 |
| #2971 | 13 |