Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #14272054 | C2 | semidirect |
| 4. #14272053 | C2 | semidirect |
| 9. #11745214 | C4 | semidirect |
| 15. D29⋊C16 | C4 | semidirect |
| 16. C29×M32 | C4 | semidirect |
| 17. #11745160 | C4 | semidirect |
| 19. C16×D29 | C4 | semidirect |
| 35. #90770 | C2×C4 | semidirect |
| 36. C16×C29 | C2×C4 | semidirect |
| 37. #90768 | C2×C4 | semidirect |
| 73. D29 | #347 | semidirect |
| 81. M32 | #1181 | semidirect |
| 88. C29 | C2×#347 | semidirect |
| 106. C16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊M32 | 2 |
| C2×#11745208 | 2 |
| #14272054 | 2 |
| #14272053 | 2 |
| M32×D29 | 2 |
| C2×#347 | 29 |