Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#11924481 | C2 | semidirect |
| 2. #14557949 | C2 | semidirect |
| 3. #14557809 | C2 | semidirect |
| 5. #14557348 | C2 | semidirect |
| 6. #14557345 | C2 | semidirect |
| 7. C37×#368 | C2 | semidirect |
| 76. #368 | D37 | semidirect |
| 79. C37 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924481 | 2 |
| #14557949 | 2 |
| #14557809 | 2 |
| #14557804 | 2 |
| #14557348 | 2 |
| #14557345 | 2 |
| C37×#368 | 2 |
| #2223 | 37 |