Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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×#90800 | C2 | semidirect |
| 2. C23×#6599 | C2 | semidirect |
| 3. #14272194 | C2 | direct (N × H) |
| 4. C2×#11745220 | C2 | semidirect |
| 5. C2×C22⋊#6599 | C2 | semidirect |
| 6. C2×C22⋊#6599 | C2 | semidirect |
| 7. C2×#11745218 | C2 | semidirect |
| 13. C2×#90800 | C22 | semidirect |
| 19. C22×#6599 | C22 | semidirect |
| 26. C22⋊#6599 | C22 | semidirect |
| 27. C22⋊#6599 | C22 | semidirect |
| 28. #11745220 | C22 | semidirect |
| 29. #11745218 | C22 | semidirect |
| 52. C2×#6599 | D4 | semidirect |
| 67. C23×C29 | M16 | semidirect |
| 93. #6599 | C2×D4 | semidirect |
| 104. C22×C29 | C2×M16 | semidirect |
| 124. C2×C29 | #435 | semidirect |
| 149. C29 | C2×#435 | semidirect |
| 187. C23 | #90800 | semidirect |
| 224. C22 | C2×#90800 | semidirect |
| 235. C2 | #14272194 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| C23×#6599 | 2 |
| #14272194 | 2 |
| C2×#11745220 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×#11745218 | 2 |
| C2×D4×Dic29 | 2 |
| C2×#435 | 29 |