Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11924528 | C2 | semidirect |
| 2. #14557833 | C2 | direct (N × H) |
| 3. C2×#11924469 | C2 | semidirect |
| 4. C2×#11924467 | C2 | semidirect |
| 5. C2×C4⋊#64436 | C2 | semidirect |
| 12. #11924528 | C22 | semidirect |
| 17. #11924469 | C22 | semidirect |
| 18. #11924467 | C22 | semidirect |
| 19. C4⋊#64436 | C22 | semidirect |
| 100. C2×C37 | #478 | semidirect |
| 112. C37 | C2×#478 | semidirect |
| 203. C2 | #14557833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924528 | 2 |
| #14557833 | 2 |
| C2×#11924469 | 2 |
| C2×#11924467 | 2 |
| C2×C4⋊#64436 | 2 |
| C2×#11924457 | 2 |
| C2×C4×D4×C37 | 2 |
| C2×#478 | 37 |