Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
616 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 616 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. C22×D232 | C2 | semidirect |
| 2. C2×#11745292 | C2 | semidirect |
| 3. #14271399 | C2 | direct (N × H) |
| 4. C2×#11745166 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C23×C8×C29 | C2 | semidirect |
| 13. C22×C8×C29 | C22 | semidirect |
| 15. #11745292 | C22 | semidirect |
| 19. C2×D232 | C22 | semidirect |
| 20. #11745169 | C22 | semidirect |
| 21. #11745166 | C22 | semidirect |
| 39. C2×C8×C29 | D4 | semidirect |
| 48. C23×C29 | D8 | semidirect |
| 71. C8×C29 | C2×D4 | semidirect |
| 78. C22×C29 | C2×D8 | semidirect |
| 91. C23×C8 | D29 | semidirect |
| 97. C2×C29 | #466 | semidirect |
| 110. C22×C8 | C2×D29 | semidirect |
| 117. C29 | C2×#466 | semidirect |
| 136. C2×C8 | C22⋊D29 | semidirect |
| 148. C23 | D232 | semidirect |
| 167. C8 | C2×C22⋊D29 | semidirect |
| 176. C22 | C2×D232 | semidirect |
| 187. C2 | #14271399 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745292 | 2 |
| #14271399 | 2 |
| C2×#11745166 | 2 |
| C2×#11745169 | 2 |
| C23×C8×C29 | 2 |
| C2×#466 | 29 |