Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 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×#11924535 | C2 | semidirect |
| 3. #14557821 | C2 | direct (N × H) |
| 4. C2×#11924468 | C2 | semidirect |
| 5. C2×#11924467 | C2 | semidirect |
| 6. C2×#11924465 | C2 | semidirect |
| 13. #11924535 | C22 | semidirect |
| 21. #11924468 | C22 | semidirect |
| 22. #11924467 | C22 | semidirect |
| 23. #11924465 | C22 | semidirect |
| 32. C2×D4×C37 | Q8 | semidirect |
| 65. D4×C37 | C2×Q8 | semidirect |
| 102. C2×C37 | #476 | semidirect |
| 114. C37 | C2×#476 | semidirect |
| 140. C2×D4 | Dic74 | semidirect |
| 172. D4 | C2×Dic74 | semidirect |
| 207. C2 | #14557821 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924535 | 2 |
| C2×D4×Dic37 | 2 |
| #14557821 | 2 |
| C2×#11924468 | 2 |
| C2×#11924467 | 2 |
| C2×#11924465 | 2 |
| C2×#11924457 | 2 |
| C2×#102×C37 | 2 |
| C2×#476 | 37 |