Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 186 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×#90796 | C2 | semidirect |
| 2. C22×#90800 | C2 | semidirect |
| 3. #14272196 | C2 | direct (N × H) |
| 4. C2×#11745220 | C2 | semidirect |
| 5. C2×#11745219 | C2 | semidirect |
| 6. C2×C22⋊#6599 | C2 | semidirect |
| 7. C2×C4×#6599 | C2 | semidirect |
| 13. C2×#90800 | C22 | semidirect |
| 19. C2×#90796 | C22 | semidirect |
| 26. C22⋊#6599 | C22 | semidirect |
| 27. #11745220 | C22 | semidirect |
| 28. #11745219 | C22 | semidirect |
| 29. C4×#6599 | C22 | semidirect |
| 51. C2×#6599 | D4 | semidirect |
| 80. C2×Dic29 | M16 | semidirect |
| 93. #6599 | C2×D4 | semidirect |
| 111. Dic29 | C2×M16 | semidirect |
| 123. C2×C29 | #436 | semidirect |
| 149. C29 | C2×#436 | semidirect |
| 235. C2 | #14272196 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| C22×#90800 | 2 |
| #14272196 | 2 |
| C2×#11745220 | 2 |
| C2×#11745219 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×C4×#6599 | 2 |
| C2×#11745243 | 2 |
| C2×#436 | 29 |