Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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. #11719136 | C2 | semidirect |
| 4. #11719135 | C2 | semidirect |
| 5. #11719083 | C2 | semidirect |
| 6. #11719071 | C2 | semidirect |
| 7. C4×C4⋊#261 | C2 | semidirect |
| 8. #11719057 | C2 | semidirect |
| 17. C4×D4×C13 | C4 | semidirect |
| 18. D4×Dic13 | C4 | semidirect |
| 19. C4×C22⋊D13 | C4 | semidirect |
| 20. #88147 | C4 | semidirect |
| 22. #88135 | C4 | semidirect |
| 24. C4×D52 | C4 | semidirect |
| 141. C4×D4 | #261 | semidirect |
| 197. C13 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D13 | 2 |
| #11719151 | 2 |
| #11719136 | 2 |
| #11719135 | 2 |
| #11719083 | 2 |
| #11719071 | 2 |
| C4×C4⋊#261 | 2 |
| #11719057 | 2 |
| #2319 | 13 |