Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10596942 | C2 | semidirect |
| 4. #14557772 | C2 | direct (N × H) |
| 5. C2×#11924469 | C2 | semidirect |
| 6. C2×#11924460 | C2 | semidirect |
| 7. C2×#11924459 | C2 | semidirect |
| 11. C2×#10596942 | C22 | semidirect |
| 21. #11924469 | C22 | semidirect |
| 22. #11924460 | C22 | semidirect |
| 23. #11924459 | C22 | semidirect |
| 66. C23×C37 | Q16 | semidirect |
| 99. C22×C37 | C2×Q16 | semidirect |
| 112. C2×C37 | #467 | semidirect |
| 124. C37 | C2×#467 | semidirect |
| 182. C23 | #10596942 | semidirect |
| 215. C22 | C2×#10596942 | semidirect |
| 227. C2 | #14557772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596942 | 2 |
| C23×#64436 | 2 |
| C2×#11924515 | 2 |
| #14557772 | 2 |
| C2×#11924469 | 2 |
| C2×#11924460 | 2 |
| C2×#11924459 | 2 |
| C2×C22⋊Q8×C37 | 2 |
| C2×#467 | 37 |