Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. C2×#88104 | C2 | semidirect |
| 4. #11719092 | C2 | semidirect |
| 5. #11718274 | C2 | semidirect |
| 9. C13×#131 | C4 | semidirect |
| 10. #88202 | C4 | semidirect |
| 12. #88161 | C4 | semidirect |
| 16. #88155 | C4 | semidirect |
| 117. #131 | #261 | semidirect |
| 171. C13 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#131 | 2 |
| #11719166 | 2 |
| C2×#88104 | 2 |
| #11719092 | 2 |
| #11718274 | 2 |
| #1814 | 13 |