Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 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×#11924477 | C2 | semidirect |
| 3. #14557803 | C2 | semidirect |
| 4. #14557346 | C2 | semidirect |
| 5. #14557340 | C2 | semidirect |
| 6. #14557317 | C2 | semidirect |
| 7. C37×#576 | C2 | semidirect |
| 9. C2×D296 | C22 | semidirect |
| 13. #11924476 | C22 | semidirect |
| 14. C2×#10596925 | C22 | semidirect |
| 15. #11924472 | C22 | semidirect |
| 94. #576 | D37 | semidirect |
| 101. C37 | #2192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557968 | 2 |
| C2×#11924477 | 2 |
| #14557803 | 2 |
| #14557346 | 2 |
| #14557340 | 2 |
| #14557317 | 2 |
| C37×#576 | 2 |
| #2192 | 37 |