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. #11718292 | C2 | semidirect |
| 5. #11718241 | C2 | semidirect |
| 7. C2×#6129 | C4 | semidirect |
| 10. C13×#121 | C4 | semidirect |
| 14. #88178 | C4 | semidirect |
| 16. #88146 | C4 | semidirect |
| 29. C2×D4×C13 | C2×C4 | semidirect |
| 41. C2×Dic26 | C2×C4 | semidirect |
| 44. C13×C4⋊C4 | C2×C4 | semidirect |
| 51. C4⋊Dic13 | C2×C4 | semidirect |
| 125. #121 | #261 | semidirect |
| 148. C2×D4 | 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 |
|---|---|
| #11719311 | 2 |
| C2×(C2×#261)⋊C4 | 2 |
| #11719127 | 2 |
| #11718292 | 2 |
| #11718241 | 2 |
| #1504 | 13 |