Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #14557815 | C2 | semidirect |
| 3. C8×Dic74 | C2 | semidirect |
| 4. #14557284 | C2 | semidirect |
| 5. #14557279 | C2 | semidirect |
| 57. Dic74 | SD16 | semidirect |
| 59. C8×C37 | SD16 | semidirect |
| 87. C37 | #1666 | semidirect |
| 142. C8 | #10596940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557815 | 2 |
| #14557730 | 2 |
| C8×Dic74 | 2 |
| #14557284 | 2 |
| #14557279 | 2 |
| #14557277 | 2 |
| C37×#492 | 2 |
| #1666 | 37 |