Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#11745183 | C2 | semidirect |
| 5. #14270925 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 7. C2×C4×Q8×C29 | C2 | semidirect |
| 18. C2×#90784 | C4 | semidirect |
| 73. Q8×C29 | C22⋊C4 | semidirect |
| 85. C2×C4×C29 | SD16 | semidirect |
| 126. C2×C4×Q8 | D29 | semidirect |
| 158. C29 | #1880 | semidirect |
| 206. Q8 | #90781 | semidirect |
| 225. C2×C4 | #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×#11745183 | 2 |
| C2×#11745157 | 2 |
| #14271065 | 2 |
| #14270925 | 2 |
| #14270918 | 2 |
| C2×C4×Q8×C29 | 2 |
| #1880 | 29 |