Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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×C8×#261 | C2 | semidirect |
| 4. #11719079 | C2 | semidirect |
| 6. #11718268 | C2 | semidirect |
| 7. #11718247 | C2 | semidirect |
| 21. C13×#102 | C4 | semidirect |
| 22. #88072 | C4 | semidirect |
| 23. #88056 | C4 | semidirect |
| 24. #88050 | C4 | semidirect |
| 120. #102 | #261 | semidirect |
| 160. C13 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719147 | 2 |
| C2×#88116 | 2 |
| C2×C8×#261 | 2 |
| #11719079 | 2 |
| #11718433 | 2 |
| #11718268 | 2 |
| #11718247 | 2 |
| #1937 | 13 |