Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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×C8×D37 | C2 | semidirect |
| 3. C2×#11924448 | C2 | semidirect |
| 4. C2×#11924448 | C2 | semidirect |
| 5. C2×#11924448 | C2 | semidirect |
| 6. #14557288 | C2 | semidirect |
| 7. C37×#336 | C2 | semidirect |
| 36. C2×D148 | C8 | semidirect |
| 54. C2×C8×C37 | D4 | semidirect |
| 65. C2×#64436 | D4 | semidirect |
| 80. C22×D37 | C2×C8 | semidirect |
| 87. C2×C4×C37 | C2×C8 | semidirect |
| 133. C2×D37 | C22⋊C8 | semidirect |
| 158. #336 | D37 | semidirect |
| 159. C37 | #1869 | semidirect |
| 213. C2×C8 | D148 | semidirect |
| 254. C2×C4 | C8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D37 | 2 |
| C2×C4×D148 | 2 |
| C2×#11924448 | 2 |
| #14557288 | 2 |
| C37×#336 | 2 |
| #1869 | 37 |