Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719223 | C2 | semidirect |
| 3. #11718737 | C2 | semidirect |
| 4. #11718732 | C2 | semidirect |
| 5. #11718730 | C2 | semidirect |
| 6. #11718725 | C2 | semidirect |
| 7. #11718703 | C2 | semidirect |
| 8. #11718702 | C2 | semidirect |
| 9. #11718679 | C2 | semidirect |
| 10. C4×#6105 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 176. C13 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#540 | 2 |
| #11719223 | 2 |
| #11718737 | 2 |
| #11718732 | 2 |
| #11718730 | 2 |
| #11718725 | 2 |
| #11718703 | 2 |
| #11718702 | 2 |
| #11718679 | 2 |
| C4×#6105 | 2 |
| #11718658 | 2 |
| #3174 | 13 |