Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11719282 | C2 | semidirect |
| 2. C8×Q8×C13 | C2 | semidirect |
| 3. #11718504 | C2 | semidirect |
| 4. #11718356 | C2 | semidirect |
| 5. C4×D104 | C2 | semidirect |
| 33. Q8×C13 | D8 | semidirect |
| 44. C8×C13 | #41 | semidirect |
| 48. C8×Q8 | D13 | semidirect |
| 88. C13 | #3391 | semidirect |
| 90. Q8 | D104 | semidirect |
| 101. C8 | #6131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719282 | 2 |
| C8×Q8×C13 | 2 |
| #11718504 | 2 |
| #11718356 | 2 |
| C4×D104 | 2 |
| #3391 | 13 |