Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #14557903 | C2 | semidirect |
| 4. #14557902 | C2 | semidirect |
| 5. #14557901 | C2 | semidirect |
| 6. #14557900 | C2 | semidirect |
| 9. C37×#491 | C2 | semidirect |
| 87. D37 | #491 | direct (N × H) |
| 94. #491 | D37 | direct (N × H) |
| 97. C37 | C2×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D37 | 2 |
| #125×D37 | 2 |
| #14557903 | 2 |
| #14557902 | 2 |
| #14557901 | 2 |
| #14557900 | 2 |
| #103×D37 | 2 |
| #97×D37 | 2 |
| C37×#491 | 2 |
| C2×#491 | 37 |