Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
560 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 3. #11718872 | C2 | semidirect |
| 4. C4×C22⋊Dic13 | C2 | semidirect |
| 5. C4⋊C4×Dic13 | C2 | semidirect |
| 6. #11718612 | C2 | semidirect |
| 7. #11718597 | C2 | semidirect |
| 8. C4×C4⋊Dic13 | C2 | semidirect |
| 11. C4×D4×C13 | C4 | semidirect |
| 102. C4×D4 | Dic13 | semidirect |
| 145. C13 | #2357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| #11718882 | 2 |
| #11718872 | 2 |
| C4×C22⋊Dic13 | 2 |
| C4⋊C4×Dic13 | 2 |
| #11718612 | 2 |
| #11718597 | 2 |
| C4×C4⋊Dic13 | 2 |
| #2357 | 13 |