Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#88124 | C2 | semidirect |
| 3. #11718741 | C2 | semidirect |
| 4. #11718732 | C2 | semidirect |
| 5. #11718695 | C2 | semidirect |
| 6. #11718694 | C2 | semidirect |
| 7. #11718670 | C2 | semidirect |
| 8. #11718587 | C2 | semidirect |
| 168. C13 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C2×#88124 | 2 |
| #11718741 | 2 |
| #11718732 | 2 |
| #11718695 | 2 |
| #11718694 | 2 |
| #11718670 | 2 |
| #11718587 | 2 |
| #3234 | 13 |