Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#90785 | C2 | semidirect |
| 4. #14271385 | C2 | direct (N × H) |
| 5. C2×C4⋊#6597 | C2 | semidirect |
| 6. C2×#11745158 | C2 | semidirect |
| 8. C2×C4×Q8×C29 | C2 | semidirect |
| 13. C4×Q8×C29 | C22 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 28. #11745158 | C22 | semidirect |
| 30. C4⋊#6597 | C22 | semidirect |
| 114. C2×C4×Q8 | D29 | semidirect |
| 119. C2×C29 | #464 | semidirect |
| 136. C4×Q8 | C2×D29 | semidirect |
| 146. C29 | C2×#464 | semidirect |
| 227. C2 | #14271385 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C22×#90784 | 2 |
| C2×#11745237 | 2 |
| #14271385 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745158 | 2 |
| C2×#11745157 | 2 |
| C2×C4×Q8×C29 | 2 |
| C2×#464 | 29 |