Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14558331 | C2 | semidirect |
| 2. C2×#11924564 | C2 | semidirect |
| 3. #14558097 | C2 | semidirect |
| 4. #14557537 | C2 | semidirect |
| 5. #14557506 | C2 | semidirect |
| 6. #14557305 | C2 | semidirect |
| 7. C37×#421 | C2 | semidirect |
| 53. C2×D148 | D4 | semidirect |
| 55. C2×Dic74 | D4 | semidirect |
| 57. M16×C37 | D4 | semidirect |
| 72. C2×#64436 | D4 | semidirect |
| 146. #421 | D37 | semidirect |
| 150. C37 | #2008 | semidirect |
| 208. M16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558331 | 2 |
| C2×#11924564 | 2 |
| #14558097 | 2 |
| #14557537 | 2 |
| #14557506 | 2 |
| #14557305 | 2 |
| C37×#421 | 2 |
| #2008 | 37 |