Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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×#88172 | C2 | semidirect |
| 2. #11719432 | C2 | semidirect |
| 4. C13×#494 | C2 | semidirect |
| 5. #11718850 | C2 | semidirect |
| 6. #11718848 | C2 | semidirect |
| 7. #11718847 | C2 | semidirect |
| 8. #11718751 | C2 | semidirect |
| 9. #11718744 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. #11718349 | C2 | semidirect |
| 80. #6095 | D4 | semidirect |
| 116. #494 | D13 | semidirect |
| 134. C4×C13 | #137 | semidirect |
| 216. C13 | #3276 | semidirect |
| 261. C4 | #88172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88172 | 2 |
| #11719432 | 2 |
| #11719431 | 2 |
| C13×#494 | 2 |
| #11718850 | 2 |
| #11718848 | 2 |
| #11718847 | 2 |
| #11718751 | 2 |
| #11718744 | 2 |
| C4×#6095 | 2 |
| #11718349 | 2 |
| #3276 | 13 |