Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 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. #14557968 | C2 | semidirect |
| 2. C2×#11924479 | C2 | semidirect |
| 3. #14557803 | C2 | semidirect |
| 4. #14557349 | C2 | semidirect |
| 5. #14557340 | C2 | semidirect |
| 6. #14557317 | C2 | semidirect |
| 7. C37×#578 | C2 | semidirect |
| 91. #578 | D37 | semidirect |
| 98. C37 | #2193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557968 | 2 |
| C2×#11924479 | 2 |
| #14557803 | 2 |
| #14557349 | 2 |
| #14557340 | 2 |
| #14557317 | 2 |
| C37×#578 | 2 |
| #2193 | 37 |