Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11745169 | C2 | semidirect |
| 3. #14271023 | C2 | semidirect |
| 4. #14270926 | C2 | semidirect |
| 5. C23×C8×C29 | C2 | semidirect |
| 14. #11745292 | C4 | semidirect |
| 40. C2×C8×C29 | D4 | semidirect |
| 83. C22×C29 | #102 | semidirect |
| 100. C23×C8 | D29 | semidirect |
| 126. C29 | #1893 | semidirect |
| 147. C2×C8 | C22⋊D29 | semidirect |
| 194. C22 | #11745169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| C2×#11745169 | 2 |
| #14271023 | 2 |
| #14270926 | 2 |
| C23×C8×C29 | 2 |
| #1893 | 29 |