Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#11924477 | C2 | semidirect |
| 2. C22×#10596925 | C2 | semidirect |
| 3. #14557769 | C2 | semidirect |
| 4. #14557358 | C2 | semidirect |
| 5. #14557334 | C2 | semidirect |
| 6. #14557333 | C2 | semidirect |
| 7. C37×#466 | C2 | semidirect |
| 39. #10596925 | D4 | semidirect |
| 63. C22×C37 | D16 | semidirect |
| 83. #466 | D37 | semidirect |
| 87. C37 | #2215 | semidirect |
| 146. C22 | #11924477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924477 | 2 |
| C22×#10596925 | 2 |
| #14557769 | 2 |
| #14557358 | 2 |
| #14557334 | 2 |
| #14557333 | 2 |
| C37×#466 | 2 |
| #2215 | 37 |