Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 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. #11718725 | C2 | semidirect |
| 4. #11718717 | C2 | semidirect |
| 5. #11718705 | C2 | semidirect |
| 6. #11718704 | C2 | semidirect |
| 9. #11718683 | C2 | semidirect |
| 10. #11718670 | C2 | semidirect |
| 11. #11718586 | C2 | semidirect |
| 203. C13 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| C2×#88124 | 2 |
| #11718725 | 2 |
| #11718717 | 2 |
| #11718705 | 2 |
| #11718704 | 2 |
| #11718695 | 2 |
| #11718694 | 2 |
| #11718683 | 2 |
| #11718670 | 2 |
| #11718586 | 2 |
| #3232 | 13 |