Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#90773 | C2 | semidirect |
| 2. C2×#11745286 | C2 | semidirect |
| 4. C2×#11745164 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. #14270926 | C2 | semidirect |
| 7. C2×C29×C22⋊C8 | C2 | semidirect |
| 56. C2×Dic58 | D4 | semidirect |
| 62. C2×C8×C29 | D4 | semidirect |
| 68. C4⋊Dic29 | D4 | semidirect |
| 77. C23×C29 | SD16 | semidirect |
| 154. C2×C22⋊C8 | D29 | semidirect |
| 186. C29 | #2000 | semidirect |
| 221. C2×C8 | C22⋊D29 | semidirect |
| 242. C23 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745286 | 2 |
| C2×#11745292 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| #14270926 | 2 |
| C2×C29×C22⋊C8 | 2 |
| #2000 | 29 |