Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #11719272 | C2 | semidirect |
| 3. C13×#446 | C2 | semidirect |
| 4. #11718512 | C2 | semidirect |
| 5. #11718511 | C2 | semidirect |
| 9. #11718363 | C2 | semidirect |
| 11. #11718343 | C2 | semidirect |
| 72. #6095 | Q8 | semidirect |
| 94. Dic26 | C2×Q8 | semidirect |
| 97. C8×C13 | C2×Q8 | semidirect |
| 106. #446 | D13 | semidirect |
| 189. C13 | #3386 | semidirect |
| 213. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| #11719272 | 2 |
| C13×#446 | 2 |
| #11718512 | 2 |
| #11718511 | 2 |
| #11718508 | 2 |
| #11718507 | 2 |
| #11718371 | 2 |
| #11718363 | 2 |
| C4×#6095 | 2 |
| #11718343 | 2 |
| #3386 | 13 |