Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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×#88173 | C2 | semidirect |
| 2. #11719431 | C2 | semidirect |
| 3. #11719282 | C2 | semidirect |
| 4. C13×#462 | C2 | semidirect |
| 5. #11718848 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. C4×#6106 | C2 | semidirect |
| 8. #11718504 | C2 | semidirect |
| 9. #11718495 | C2 | semidirect |
| 10. #11718472 | C2 | semidirect |
| 11. #11718468 | C2 | semidirect |
| 70. #6106 | D4 | semidirect |
| 121. #462 | D13 | semidirect |
| 141. C4×C13 | #135 | semidirect |
| 222. C13 | #3284 | semidirect |
| 272. C4 | #88173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| #11719431 | 2 |
| #11719282 | 2 |
| C13×#462 | 2 |
| #11718848 | 2 |
| #11718746 | 2 |
| C4×#6106 | 2 |
| #11718504 | 2 |
| #11718495 | 2 |
| #11718472 | 2 |
| #11718468 | 2 |
| #3284 | 13 |