Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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×#90785 | C2 | semidirect |
| 4. #14271402 | C2 | direct (N × H) |
| 5. C2×#11745155 | C2 | semidirect |
| 6. C2×#11745183 | C2 | semidirect |
| 7. C2×#11745158 | C2 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 28. #11745183 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 66. C23×C29 | Q16 | semidirect |
| 100. C22×C29 | C2×Q16 | semidirect |
| 120. C2×C29 | #467 | semidirect |
| 146. C29 | C2×#467 | semidirect |
| 182. C23 | #90785 | semidirect |
| 215. C22 | C2×#90785 | semidirect |
| 227. C2 | #14271402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C23×#6597 | 2 |
| C2×#11745286 | 2 |
| #14271402 | 2 |
| C2×#11745155 | 2 |
| C2×#11745183 | 2 |
| C2×#11745158 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C2×#467 | 29 |