Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#88111 | C2 | semidirect |
| 4. #11718240 | C2 | direct (N × H) |
| 7. C22×D52 | C4 | semidirect |
| 10. C2×C13×C4⋊C4 | C4 | semidirect |
| 14. #88149 | C4 | semidirect |
| 17. (C2×#261)⋊C4 | C22 | semidirect |
| 19. #88111 | C22 | semidirect |
| 35. C2×D52 | C2×C4 | semidirect |
| 44. C13×C4⋊C4 | C2×C4 | semidirect |
| 117. C2×C4⋊C4 | #261 | semidirect |
| 123. C2×C13 | #327 | semidirect |
| 155. C4⋊C4 | C2×#261 | semidirect |
| 158. C13 | C2×#327 | semidirect |
| 219. C2 | #11718240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88149 | 2 |
| C2×(C2×#261)⋊C4 | 2 |
| C2×#88111 | 2 |
| #11718240 | 2 |
| C2×#327 | 13 |