Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
908 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 253 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×#90779 | C2 | semidirect |
| 4. #14271098 | C2 | direct (N × H) |
| 5. C2×#11745179 | C2 | semidirect |
| 6. C22×C4⋊C4×C29 | C2 | semidirect |
| 13. C2×C4⋊C4×C29 | C22 | semidirect |
| 19. C2×#90779 | C22 | semidirect |
| 20. #11745179 | C22 | semidirect |
| 98. C22×C4⋊C4 | D29 | semidirect |
| 103. C2×C29 | #399 | semidirect |
| 118. C2×C4⋊C4 | C2×D29 | semidirect |
| 124. C29 | C2×#399 | semidirect |
| 201. C2 | #14271098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90779 | 2 |
| C22×#90781 | 2 |
| #14271098 | 2 |
| C2×#11745179 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C2×#399 | 29 |