Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. C2×#88170 | C2 | semidirect |
| 2. #11719431 | C2 | semidirect |
| 3. #11719260 | C2 | semidirect |
| 4. C13×#461 | C2 | semidirect |
| 5. #11718834 | C2 | semidirect |
| 6. #11718753 | C2 | semidirect |
| 7. C4×#6104 | C2 | semidirect |
| 8. #11718502 | C2 | semidirect |
| 9. #11718495 | C2 | semidirect |
| 10. #11718474 | C2 | semidirect |
| 11. #11718471 | C2 | semidirect |
| 67. #6104 | D4 | semidirect |
| 120. #461 | D13 | semidirect |
| 138. C4×C13 | #135 | semidirect |
| 220. C13 | #3283 | semidirect |
| 268. C4 | #88170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88170 | 2 |
| #11719431 | 2 |
| #11719260 | 2 |
| C13×#461 | 2 |
| #11718834 | 2 |
| #11718753 | 2 |
| C4×#6104 | 2 |
| #11718502 | 2 |
| #11718495 | 2 |
| #11718474 | 2 |
| #11718471 | 2 |
| #3283 | 13 |