Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11719421 | C2 | semidirect |
| 2. #11719373 | C2 | semidirect |
| 3. C13×#496 | C2 | semidirect |
| 4. #11718833 | C2 | semidirect |
| 5. #11718823 | C2 | semidirect |
| 6. #11718819 | C2 | semidirect |
| 7. #11718811 | C2 | semidirect |
| 8. #11718735 | C2 | semidirect |
| 9. #11718716 | C2 | semidirect |
| 10. #11718375 | C2 | semidirect |
| 11. #11718366 | C2 | semidirect |
| 124. #496 | D13 | semidirect |
| 234. C13 | #3214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11719373 | 2 |
| C13×#496 | 2 |
| #11718833 | 2 |
| #11718823 | 2 |
| #11718819 | 2 |
| #11718811 | 2 |
| #11718735 | 2 |
| #11718716 | 2 |
| #11718375 | 2 |
| #11718366 | 2 |
| #3214 | 13 |