Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 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 |
|---|---|---|
| 2. C2×#88116 | C2 | semidirect |
| 3. #11719057 | C2 | semidirect |
| 4. #11719053 | C2 | semidirect |
| 8. C13×#127 | C4 | semidirect |
| 10. #88190 | C4 | semidirect |
| 13. #88123 | C4 | semidirect |
| 29. C4×#261 | D4 | semidirect |
| 75. #127 | #261 | semidirect |
| 107. C13 | #1963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| C2×#88116 | 2 |
| #11719057 | 2 |
| #11719053 | 2 |
| #1963 | 13 |