Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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. M16×#3866 | C2 | semidirect |
| 4. #14558469 | C2 | semidirect |
| 5. #14558405 | C2 | semidirect |
| 6. #14558404 | C2 | semidirect |
| 9. Q8×#3866 | C4 | semidirect |
| 11. D4×#3866 | C4 | semidirect |
| 17. #11924601 | C4 | semidirect |
| 18. #11924600 | C4 | semidirect |
| 25. #11924464 | C4 | semidirect |
| 26. #11924463 | C4 | semidirect |
| 27. #11924462 | C4 | semidirect |
| 28. #104×C37 | C4 | semidirect |
| 53. C4×#3866 | C2×C4 | semidirect |
| 56. #10596953 | C2×C4 | semidirect |
| 58. M16×C37 | C2×C4 | semidirect |
| 59. C42×C37 | C2×C4 | semidirect |
| 61. C4×Dic37 | C2×C4 | semidirect |
| 62. #10596934 | C2×C4 | semidirect |
| 134. C37 | #1759 | semidirect |
| 152. #104 | #3866 | semidirect |
| 175. M16 | C2×#3866 | semidirect |
| 191. C42 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#3866 | 2 |
| D37⋊#104 | 2 |
| M16×#3866 | 2 |
| #14558469 | 2 |
| #14558405 | 2 |
| #14558404 | 2 |
| #104×D37 | 2 |
| #1759 | 37 |