Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14557907 | C2 | semidirect |
| 3. D4×#64436 | C2 | semidirect |
| 4. #14557283 | C2 | semidirect |
| 5. #14557279 | C2 | semidirect |
| 6. #14557276 | C2 | semidirect |
| 7. C37×#474 | C2 | semidirect |
| 48. D4×C37 | SD16 | semidirect |
| 65. #64436 | D8 | semidirect |
| 87. #474 | D37 | semidirect |
| 93. C37 | #1665 | semidirect |
| 139. D4 | #10596941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557907 | 2 |
| #14557728 | 2 |
| D4×#64436 | 2 |
| #14557283 | 2 |
| #14557279 | 2 |
| #14557276 | 2 |
| C37×#474 | 2 |
| #1665 | 37 |