Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10596925 | C2 | semidirect |
| 2. C2×#11924470 | C2 | semidirect |
| 3. #14557334 | C2 | direct (N × H) |
| 7. C2×#10596925 | C22 | semidirect |
| 9. #11924470 | C22 | semidirect |
| 13. C2×D8×C37 | C4 | semidirect |
| 25. D8×C37 | C2×C4 | semidirect |
| 64. C2×C37 | #357 | semidirect |
| 72. C37 | C2×#357 | semidirect |
| 76. C2×D8 | Dic37 | semidirect |
| 93. D8 | C2×Dic37 | semidirect |
| 131. C2 | #14557334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596925 | 2 |
| C2×#11924470 | 2 |
| #14557334 | 2 |
| C22×D8×C37 | 2 |
| C2×#357 | 37 |