Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719284 | C2 | semidirect |
| 2. C8×Q8×C13 | C2 | semidirect |
| 3. #11718508 | C2 | semidirect |
| 4. #11718503 | C2 | semidirect |
| 7. #11718344 | C2 | semidirect |
| 8. #11718343 | C2 | semidirect |
| 47. D104 | Q8 | semidirect |
| 71. C8×Q8 | D13 | semidirect |
| 129. C13 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| C8×Q8×C13 | 2 |
| #11718508 | 2 |
| #11718503 | 2 |
| C4×D104 | 2 |
| #11718344 | 2 |
| #11718343 | 2 |
| #3380 | 13 |