Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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×#11924477 | C2 | semidirect |
| 2. #14557908 | C2 | semidirect |
| 3. D8×Dic37 | C2 | semidirect |
| 4. #14557351 | C2 | semidirect |
| 5. #14557335 | C2 | semidirect |
| 6. #14557334 | C2 | semidirect |
| 7. C2×D16×C37 | C2 | semidirect |
| 30. D8×C37 | D4 | semidirect |
| 74. Dic37 | D16 | semidirect |
| 83. C2×D16 | D37 | semidirect |
| 89. C37 | #2206 | semidirect |
| 115. D8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924477 | 2 |
| #14557908 | 2 |
| D8×Dic37 | 2 |
| #14557351 | 2 |
| #14557335 | 2 |
| #14557334 | 2 |
| C2×D16×C37 | 2 |
| #2206 | 37 |