Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #11719282 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. C8×Q8×C13 | C2 | semidirect |
| 4. #11718507 | C2 | semidirect |
| 5. #11718504 | C2 | semidirect |
| 6. #11718355 | C2 | semidirect |
| 7. C4×D104 | C2 | semidirect |
| 47. Q8×C13 | D8 | semidirect |
| 58. D52 | #41 | semidirect |
| 69. C8×Q8 | D13 | semidirect |
| 125. C13 | #3358 | semidirect |
| 129. Q8 | D104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719282 | 2 |
| Q8×D52 | 2 |
| C8×Q8×C13 | 2 |
| #11718507 | 2 |
| #11718504 | 2 |
| #11718355 | 2 |
| C4×D104 | 2 |
| #3358 | 13 |