Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4⋊C8×D29 | C2 | semidirect |
| 3. C4×C8×D29 | C2 | semidirect |
| 4. #14270892 | C2 | semidirect |
| 5. D4⋊#6597 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 21. C29×C4⋊C8 | C22 | semidirect |
| 22. C4×C8×C29 | C22 | semidirect |
| 25. C4⋊#6597 | C22 | semidirect |
| 26. C4×#6597 | C22 | semidirect |
| 33. D4×D29 | C8 | semidirect |
| 67. D4×C29 | C2×C8 | semidirect |
| 81. D116 | C2×C8 | semidirect |
| 123. D4⋊C8 | D29 | direct (N × H) |
| 129. D29 | D4⋊C8 | direct (N × H) |
| 145. C4⋊C8 | C2×D29 | semidirect |
| 148. C4×C8 | C2×D29 | semidirect |
| 149. C29 | C2×D4⋊C8 | semidirect |
| 193. D4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D29 | 2 |
| C4⋊C8×D29 | 2 |
| C4×C8×D29 | 2 |
| #14270892 | 2 |
| D4⋊#6597 | 2 |
| #14270890 | 2 |
| C29×D4⋊C8 | 2 |
| C2×D4⋊C8 | 29 |