Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 4. #11718779 | C2 | semidirect |
| 5. M16×Dic13 | C2 | semidirect |
| 6. #11718380 | C2 | semidirect |
| 7. #11718379 | C2 | semidirect |
| 21. #88055 | C22 | semidirect |
| 22. #88054 | C22 | semidirect |
| 23. C8×Dic13 | C22 | semidirect |
| 68. C2×Dic13 | M16 | semidirect |
| 143. C13 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic13 | 2 |
| C13×#407 | 2 |
| #11718868 | 2 |
| #11718779 | 2 |
| M16×Dic13 | 2 |
| #11718380 | 2 |
| #11718379 | 2 |
| #2920 | 13 |