Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
436 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×C4×#6597 | C2 | semidirect |
| 4. #14270917 | C2 | semidirect |
| 5. C2×C4×C8×C29 | C2 | semidirect |
| 16. #11745168 | C4 | direct (N × H) |
| 28. C2×C4×D29 | C8 | semidirect |
| 32. C2×C8×C29 | C2×C4 | semidirect |
| 40. C2×#6597 | C2×C4 | semidirect |
| 75. C2×D29 | C4×C8 | semidirect |
| 76. C4×C29 | C22⋊C8 | semidirect |
| 84. C2×C4×C8 | D29 | semidirect |
| 104. C29 | C4×C22⋊C8 | semidirect |
| 122. C2×C8 | C4×D29 | semidirect |
| 164. C4 | #11745168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D29 | 2 |
| C2×#11745168 | 2 |
| C2×C4×#6597 | 2 |
| #14270917 | 2 |
| C2×C4×C8×C29 | 2 |
| C4×C22⋊C8 | 29 |