Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#90784 | C2 | semidirect |
| 3. #14271641 | C2 | semidirect |
| 4. #14271387 | C2 | semidirect |
| 5. #14271361 | C2 | semidirect |
| 6. #14271191 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 14. C2×Q16×C29 | C22 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 19. Q8×Dic29 | C22 | semidirect |
| 29. #11745183 | C22 | semidirect |
| 30. #11745180 | C22 | semidirect |
| 32. #11745162 | C22 | semidirect |
| 38. C2×Q8×C29 | D4 | semidirect |
| 112. C2×#137 | D29 | semidirect |
| 130. C2×Q16 | C2×D29 | semidirect |
| 133. C2×SD16 | C2×D29 | semidirect |
| 149. C29 | #3043 | semidirect |
| 155. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| #14271727 | 2 |
| #14271641 | 2 |
| #14271387 | 2 |
| #14271361 | 2 |
| #14271191 | 2 |
| #14271169 | 2 |
| #14271159 | 2 |
| C2×C29×#137 | 2 |
| #3043 | 29 |