Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. C2×C22⋊#6597 | C2 | semidirect |
| 2. C2×#11745179 | C2 | semidirect |
| 3. #14270897 | C2 | direct (N × H) |
| 6. C22×D4×C29 | C4 | semidirect |
| 11. C29×#121 | C4 | semidirect |
| 13. C2×C4⋊C4×C29 | C4 | semidirect |
| 17. #11745179 | C22 | semidirect |
| 19. C22⋊#6597 | C22 | semidirect |
| 28. C2×D4×C29 | C2×C4 | semidirect |
| 42. C4⋊C4×C29 | C2×C4 | semidirect |
| 112. C2×C29 | #327 | semidirect |
| 117. C22×D4 | Dic29 | semidirect |
| 123. #121 | Dic29 | semidirect |
| 125. C2×C4⋊C4 | Dic29 | semidirect |
| 131. C29 | C2×#327 | semidirect |
| 140. C2×D4 | C2×Dic29 | semidirect |
| 156. C4⋊C4 | C2×Dic29 | semidirect |
| 219. C2 | #14270897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#6597 | 2 |
| C2×#11745179 | 2 |
| #14270897 | 2 |
| C2×C29×#121 | 2 |
| C2×#327 | 29 |