Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14557358 | C2 | semidirect |
| 4. #14557337 | C2 | semidirect |
| 6. #14557309 | C2 | semidirect |
| 7. C4×Q16×C37 | C2 | semidirect |
| 10. #11924479 | C4 | semidirect |
| 24. Q16×C37 | C2×C4 | semidirect |
| 36. #10596925 | C2×C4 | semidirect |
| 69. C4×Q16 | D37 | semidirect |
| 75. C37 | #2175 | semidirect |
| 92. Q16 | C4×D37 | semidirect |
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 |
| #14557358 | 2 |
| #14557337 | 2 |
| #14557333 | 2 |
| #14557309 | 2 |
| C4×Q16×C37 | 2 |
| #2175 | 37 |