Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. C23×Dic58 | C2 | semidirect |
| 2. C22×#90783 | C2 | semidirect |
| 3. #14271301 | C2 | direct (N × H) |
| 4. C2×#11745158 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 15. C22×Dic58 | C22 | semidirect |
| 21. C2×#90783 | C22 | semidirect |
| 23. C22⋊#6597 | C22 | semidirect |
| 24. #11745158 | C22 | semidirect |
| 47. C2×Dic58 | D4 | semidirect |
| 61. C23×C29 | SD16 | semidirect |
| 82. Dic58 | C2×D4 | semidirect |
| 94. C22×C29 | C2×SD16 | semidirect |
| 110. C2×C29 | #448 | semidirect |
| 132. C29 | C2×#448 | semidirect |
| 169. C23 | #90783 | semidirect |
| 200. C22 | C2×#90783 | semidirect |
| 211. C2 | #14271301 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C22×#90783 | 2 |
| #14271301 | 2 |
| C2×#11745158 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×#121 | 2 |
| C2×#448 | 29 |