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. C13×#550 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. #11718733 | C2 | semidirect |
| 4. #11718731 | C2 | semidirect |
| 5. Q8×#1055 | C2 | semidirect |
| 6. C4×#6104 | C2 | semidirect |
| 7. #11718668 | C2 | semidirect |
| 47. Q8×C13 | D8 | semidirect |
| 59. D52 | #41 | semidirect |
| 64. #550 | D13 | semidirect |
| 125. C13 | #3358 | semidirect |
| 129. Q8 | #6104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| Q8×D52 | 2 |
| #11718733 | 2 |
| #11718731 | 2 |
| Q8×#1055 | 2 |
| C4×#6104 | 2 |
| #11718668 | 2 |
| #3358 | 13 |