Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #14557360 | C2 | semidirect |
| 4. #14557337 | C2 | semidirect |
| 6. C4×#10596925 | C2 | semidirect |
| 7. C4×Q16×C37 | C2 | semidirect |
| 10. #11924479 | C4 | direct (N × H) |
| 24. Q16×C37 | C2×C4 | semidirect |
| 36. #10596925 | C2×C4 | semidirect |
| 59. C4×C37 | SD32 | semidirect |
| 69. C4×Q16 | D37 | semidirect |
| 75. C37 | C4×SD32 | semidirect |
| 92. Q16 | C4×D37 | semidirect |
| 128. C4 | #11924479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924479 | 2 |
| C4×D296 | 2 |
| #14557360 | 2 |
| #14557337 | 2 |
| #14557333 | 2 |
| C4×#10596925 | 2 |
| C4×Q16×C37 | 2 |
| C4×SD32 | 37 |