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. #14271605 | C2 | direct (N × H) |
| 4. C2×#11745177 | C2 | semidirect |
| 5. C2×#11745148 | C2 | semidirect |
| 6. C2×#11745176 | C2 | semidirect |
| 7. C2×#11745146 | C2 | semidirect |
| 8. C2×C29×Q32 | C2 | semidirect |
| 18. Q16×D29 | C22 | semidirect |
| 22. C29×Q32 | C22 | semidirect |
| 24. #11745177 | C22 | semidirect |
| 25. #11745176 | C22 | semidirect |
| 27. #11745148 | C22 | semidirect |
| 28. #11745146 | C22 | semidirect |
| 98. C2×Q32 | D29 | semidirect |
| 102. C2×C29 | #510 | semidirect |
| 120. Q32 | C2×D29 | semidirect |
| 126. C29 | C2×#510 | semidirect |
| 193. C2 | #14271605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C2×Q16×D29 | 2 |
| #14271605 | 2 |
| C2×#11745177 | 2 |
| C2×#11745148 | 2 |
| C2×#11745176 | 2 |
| C2×#11745146 | 2 |
| C2×C29×Q32 | 2 |
| C2×#510 | 29 |