Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
182 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14557880 | C2 | semidirect |
| 2. #14557739 | C2 | semidirect |
| 4. C8×D148 | C2 | semidirect |
| 5. #14557280 | C2 | semidirect |
| 6. #14557276 | C2 | semidirect |
| 7. C37×#335 | C2 | semidirect |
| 89. #335 | D37 | semidirect |
| 92. C37 | #1681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557880 | 2 |
| #14557739 | 2 |
| #14557729 | 2 |
| C8×D148 | 2 |
| #14557280 | 2 |
| #14557276 | 2 |
| C37×#335 | 2 |
| #1681 | 37 |