Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 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×#90782 | C2 | semidirect |
| 2. C2×#11745302 | C2 | semidirect |
| 3. C2×#11745169 | C2 | semidirect |
| 4. C2×#11745180 | C2 | semidirect |
| 5. #14271066 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C22×D8×C29 | C2 | semidirect |
| 41. C2×D4×C29 | D4 | semidirect |
| 57. C2×C8×C29 | D4 | semidirect |
| 66. C2×#6597 | D4 | semidirect |
| 102. C2×Dic29 | D8 | semidirect |
| 137. C22×D8 | D29 | semidirect |
| 170. C29 | #2011 | semidirect |
| 194. C2×D4 | C22⋊D29 | semidirect |
| 205. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×#11745302 | 2 |
| C2×#11745169 | 2 |
| C2×#11745180 | 2 |
| #14271066 | 2 |
| #14270917 | 2 |
| C22×D8×C29 | 2 |
| #2011 | 29 |