Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 15. C13×#107 | C4 | semidirect |
| 16. #88058 | C4 | semidirect |
| 17. #88048 | C4 | semidirect |
| 79. #107 | #261 | semidirect |
| 108. C13 | #1945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88104 | 2 |
| C2×C8×#261 | 2 |
| #11719079 | 2 |
| #11718541 | 2 |
| #11718247 | 2 |
| #1945 | 13 |