Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#10596930 | C2 | semidirect |
| 2. C22×D296 | C2 | semidirect |
| 3. C2×#11924533 | C2 | semidirect |
| 4. C2×#11924524 | C2 | semidirect |
| 5. #14557922 | C2 | direct (N × H) |
| 6. C2×#97×C37 | C2 | semidirect |
| 12. C2×#10596930 | C22 | semidirect |
| 14. C2×D296 | C22 | semidirect |
| 16. #11924533 | C22 | semidirect |
| 18. #11924524 | C22 | semidirect |
| 22. #97×C37 | C22 | semidirect |
| 40. C2×C8×C37 | D4 | semidirect |
| 69. C8×C37 | C2×D4 | semidirect |
| 84. C2×C37 | #496 | semidirect |
| 94. C2×#97 | D37 | semidirect |
| 95. C37 | C2×#496 | semidirect |
| 111. #97 | C2×D37 | semidirect |
| 131. C2×C8 | D148 | semidirect |
| 158. C8 | C2×D148 | semidirect |
| 174. C2 | #14557922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| C22×D296 | 2 |
| C2×#11924533 | 2 |
| C2×#11924524 | 2 |
| #14557922 | 2 |
| C2×#97×C37 | 2 |
| C2×#496 | 37 |