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×#10596953 | C2 | semidirect |
| 2. C23×#64438 | C2 | semidirect |
| 3. #14558562 | C2 | direct (N × H) |
| 4. C2×C4⋊#64438 | C2 | semidirect |
| 5. C2×#11924593 | C2 | semidirect |
| 6. C2×C22⋊#64438 | C2 | semidirect |
| 7. C2×#11924591 | C2 | semidirect |
| 10. C2×#10596953 | C22 | semidirect |
| 16. C22×#64438 | C22 | semidirect |
| 17. C4⋊#64438 | C22 | semidirect |
| 18. #11924593 | C22 | semidirect |
| 19. C22⋊#64438 | C22 | semidirect |
| 20. #11924591 | C22 | semidirect |
| 51. C2×#64438 | D4 | semidirect |
| 64. C23×C37 | M16 | semidirect |
| 93. #64438 | C2×D4 | semidirect |
| 99. C22×C37 | C2×M16 | semidirect |
| 115. C2×C37 | #435 | semidirect |
| 128. C37 | C2×#435 | semidirect |
| 188. C23 | #10596953 | semidirect |
| 223. C22 | C2×#10596953 | semidirect |
| 235. C2 | #14558562 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596953 | 2 |
| C23×#64438 | 2 |
| #14558562 | 2 |
| C2×C4⋊#64438 | 2 |
| C2×#11924593 | 2 |
| C2×C22⋊#64438 | 2 |
| C2×#11924591 | 2 |
| C2×#11924496 | 2 |
| C2×#435 | 37 |