Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #14558007 | C2 | semidirect |
| 3. #14557551 | C2 | semidirect |
| 4. #14557549 | C2 | semidirect |
| 5. C2×#11924452 | C2 | semidirect |
| 6. #14557289 | C2 | semidirect |
| 7. C37×H(3,ℤ/4) | C2 | semidirect |
| 11. #11924533 | C4 | semidirect |
| 12. #11924524 | C4 | semidirect |
| 38. C2×D148 | C2×C4 | semidirect |
| 42. C2×Dic74 | C2×C4 | semidirect |
| 50. C42×C37 | C2×C4 | semidirect |
| 51. C42×C37 | D4 | semidirect |
| 56. C4×Dic37 | D4 | semidirect |
| 123. H(3,ℤ/4) | D37 | semidirect |
| 124. C37 | #1911 | semidirect |
| 175. C42 | C4×D37 | semidirect |
| 176. C42 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558102 | 2 |
| #14558007 | 2 |
| #14557551 | 2 |
| #14557549 | 2 |
| C2×#11924452 | 2 |
| #14557289 | 2 |
| C37×H(3,ℤ/4) | 2 |
| #1911 | 37 |