Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C22×#10596925 | C2 | semidirect |
| 3. #14557312 | C2 | direct (N × H) |
| 4. C22×C16×C37 | C2 | semidirect |
| 12. C2×#10596925 | C22 | semidirect |
| 15. C2×C16×C37 | C22 | semidirect |
| 37. C22×D37 | C16 | semidirect |
| 59. C2×D37 | C2×C16 | semidirect |
| 65. C2×C37 | C22⋊C16 | semidirect |
| 72. C22×C16 | D37 | semidirect |
| 74. C37 | C2×C22⋊C16 | semidirect |
| 85. C2×C16 | C2×D37 | semidirect |
| 135. C2 | #14557312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D37 | 2 |
| C22×#10596925 | 2 |
| #14557312 | 2 |
| C22×C16×C37 | 2 |
| C2×C22⋊C16 | 37 |