Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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×#10596957 | C2 | semidirect |
| 2. C23×#64438 | C2 | semidirect |
| 3. #14558564 | C2 | direct (N × H) |
| 4. C2×#11924603 | C2 | semidirect |
| 5. C2×C22⋊#64438 | C2 | semidirect |
| 6. C2×C22⋊#64438 | C2 | semidirect |
| 7. C2×#11924591 | C2 | semidirect |
| 10. C2×#10596957 | C22 | semidirect |
| 16. C22×#64438 | C22 | semidirect |
| 17. #11924603 | C22 | semidirect |
| 18. C22⋊#64438 | C22 | semidirect |
| 19. C22⋊#64438 | C22 | semidirect |
| 20. #11924591 | C22 | semidirect |
| 52. C2×#64438 | D4 | semidirect |
| 67. C23×C37 | M16 | semidirect |
| 93. #64438 | C2×D4 | semidirect |
| 103. C22×C37 | C2×M16 | semidirect |
| 116. C2×C37 | #435 | semidirect |
| 128. C37 | C2×#435 | semidirect |
| 187. C23 | #10596957 | semidirect |
| 223. C22 | C2×#10596957 | semidirect |
| 235. C2 | #14558564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596957 | 2 |
| C23×#64438 | 2 |
| #14558564 | 2 |
| C2×#11924603 | 2 |
| C2×C22⋊#64438 | 2 |
| C2×#11924591 | 2 |
| C2×D4×Dic37 | 2 |
| C2×#435 | 37 |