Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×D116 | C2 | semidirect |
| 3. #14270915 | C2 | semidirect |
| 4. D4⋊#6597 | C2 | semidirect |
| 5. #14270890 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 7. C8×D4×C29 | C2 | semidirect |
| 34. #90782 | C8 | direct (N × H) |
| 45. D4×C29 | C2×C8 | semidirect |
| 54. D116 | C2×C8 | semidirect |
| 59. C8×C29 | D8 | semidirect |
| 63. #6597 | C2×C8 | semidirect |
| 81. C8×D4 | D29 | semidirect |
| 106. C29 | C8×D8 | semidirect |
| 131. D4 | C8×D29 | semidirect |
| 147. C8 | #90782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90782 | 2 |
| C8×D116 | 2 |
| #14270915 | 2 |
| D4⋊#6597 | 2 |
| #14270890 | 2 |
| C8×#6597 | 2 |
| C8×D4×C29 | 2 |
| C8×D8 | 29 |