Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719247 | C2 | semidirect |
| 3. C13×#436 | C2 | semidirect |
| 4. #11718795 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 6. #11718512 | C2 | semidirect |
| 7. #11718507 | C2 | semidirect |
| 8. #11718398 | C2 | semidirect |
| 9. #11718383 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. #11718343 | C2 | semidirect |
| 100. C8×C13 | #41 | semidirect |
| 110. #436 | D13 | semidirect |
| 196. C13 | #3353 | semidirect |
| 222. C8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719260 | 2 |
| #11719247 | 2 |
| C13×#436 | 2 |
| #11718795 | 2 |
| #11718782 | 2 |
| #11718512 | 2 |
| #11718507 | 2 |
| #11718398 | 2 |
| #11718383 | 2 |
| C4×#6095 | 2 |
| #11718343 | 2 |
| #3353 | 13 |