Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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×(C2×#261)⋊C4 | C2 | semidirect |
| 3. #11719127 | C2 | semidirect |
| 4. #11718298 | C2 | semidirect |
| 5. #11718240 | C2 | semidirect |
| 7. C2×#6131 | C4 | semidirect |
| 10. C13×C22⋊Q8 | C4 | semidirect |
| 12. #88184 | C4 | semidirect |
| 16. #88146 | C4 | semidirect |
| 28. C2×Q8×C13 | C2×C4 | semidirect |
| 35. C2×D52 | C2×C4 | semidirect |
| 45. C13×C4⋊C4 | C2×C4 | semidirect |
| 51. C4⋊Dic13 | C2×C4 | semidirect |
| 123. C22⋊Q8 | #261 | semidirect |
| 144. C2×Q8 | C2×#261 | semidirect |
| 166. C4⋊C4 | C2×#261 | semidirect |
| 173. C13 | #1504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719332 | 2 |
| C2×(C2×#261)⋊C4 | 2 |
| #11719127 | 2 |
| #11718298 | 2 |
| #11718240 | 2 |
| #1504 | 13 |