Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 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×#90773 | C2 | semidirect |
| 2. C22×#90783 | C2 | semidirect |
| 3. C22×#90784 | C2 | semidirect |
| 4. C2×#11745306 | C2 | semidirect |
| 6. #14271534 | C2 | direct (N × H) |
| 7. C2×C8×Dic29 | C2 | semidirect |
| 8. C22×SD16×C29 | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 18. #11745306 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 30. C8×Dic29 | C22 | semidirect |
| 56. C2×C8×C29 | D4 | semidirect |
| 63. C2×#6597 | D4 | semidirect |
| 88. C2×Dic29 | SD16 | semidirect |
| 96. C8×C29 | C2×D4 | semidirect |
| 97. #6597 | C2×D4 | semidirect |
| 113. Dic29 | C2×SD16 | semidirect |
| 117. C22×SD16 | D29 | semidirect |
| 123. C2×C29 | #492 | semidirect |
| 139. C2×SD16 | C2×D29 | semidirect |
| 149. C29 | C2×#492 | semidirect |
| 180. C2×C8 | C22⋊D29 | semidirect |
| 216. C8 | C2×C22⋊D29 | semidirect |
| 234. C2 | #14271534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C22×#90783 | 2 |
| C22×#90784 | 2 |
| C2×#11745306 | 2 |
| C2×#11745302 | 2 |
| #14271534 | 2 |
| C2×C8×Dic29 | 2 |
| C22×SD16×C29 | 2 |
| C2×#492 | 29 |