Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×Q16×D29 | C2 | semidirect |
| 3. #14271602 | C2 | direct (N × H) |
| 4. C2×Dic232 | C2 | semidirect |
| 5. C2×#11745177 | C2 | semidirect |
| 6. C2×#11745175 | C2 | semidirect |
| 7. C2×#11745146 | C2 | semidirect |
| 8. C2×C29×SD32 | C2 | semidirect |
| 16. Q16×D29 | C22 | semidirect |
| 22. C29×SD32 | C22 | semidirect |
| 24. #11745177 | C22 | semidirect |
| 25. #11745175 | C22 | semidirect |
| 27. Dic232 | C22 | semidirect |
| 28. #11745146 | C22 | semidirect |
| 100. C2×SD32 | D29 | semidirect |
| 103. C2×C29 | #510 | semidirect |
| 122. SD32 | C2×D29 | semidirect |
| 126. C29 | C2×#510 | semidirect |
| 193. C2 | #14271602 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C2×Q16×D29 | 2 |
| #14271602 | 2 |
| C2×Dic232 | 2 |
| C2×#11745177 | 2 |
| C2×#11745175 | 2 |
| C2×#11745146 | 2 |
| C2×C29×SD32 | 2 |
| C2×#510 | 29 |