Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×C8×D29 | C2 | semidirect |
| 2. #14271670 | C2 | semidirect |
| 3. #14271401 | C2 | semidirect |
| 4. #14271396 | C2 | semidirect |
| 5. #14271389 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. C2×C29×#135 | C2 | semidirect |
| 12. C2×Q16×C29 | C22 | semidirect |
| 13. C2×SD16×C29 | C22 | semidirect |
| 14. C2×D8×C29 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 27. #11745180 | C22 | semidirect |
| 28. #11745166 | C22 | semidirect |
| 29. #11745165 | C22 | semidirect |
| 47. C2×C8×C29 | D4 | semidirect |
| 95. C2×D29 | #135 | semidirect |
| 102. C2×#135 | D29 | semidirect |
| 118. C2×Q16 | C2×D29 | semidirect |
| 119. C2×SD16 | C2×D29 | semidirect |
| 120. C2×D8 | C2×D29 | semidirect |
| 136. C29 | #3050 | semidirect |
| 158. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| #14271670 | 2 |
| #14271401 | 2 |
| #14271396 | 2 |
| #14271389 | 2 |
| #14271201 | 2 |
| #14271159 | 2 |
| C2×C29×#135 | 2 |
| #3050 | 29 |