Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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×#90784 | C2 | semidirect |
| 3. C2×#11745183 | C2 | semidirect |
| 4. C2×#11745157 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 6. #14270925 | C2 | semidirect |
| 7. C2×C29×C22⋊Q8 | C2 | semidirect |
| 36. C2×Q8×C29 | D4 | semidirect |
| 59. C4⋊C4×C29 | D4 | semidirect |
| 70. C2×#6597 | D4 | semidirect |
| 77. C23×C29 | SD16 | semidirect |
| 150. C2×C22⋊Q8 | D29 | semidirect |
| 186. C29 | #2000 | semidirect |
| 194. C2×Q8 | C22⋊D29 | semidirect |
| 226. C4⋊C4 | C22⋊D29 | semidirect |
| 242. C23 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745292 | 2 |
| C2×#11745183 | 2 |
| C2×#11745157 | 2 |
| C2×C22⋊#6597 | 2 |
| #14270925 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| #2000 | 29 |