Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 19. #11924536 | C4 | semidirect |
| 20. #11924535 | C4 | semidirect |
| 21. #11924534 | C4 | semidirect |
| 24. C4⋊Q8×C37 | C4 | semidirect |
| 44. C4×#3866 | Q8 | semidirect |
| 84. #3866 | C4⋊Q8 | direct (N × H) |
| 87. C4×C37 | C4×Q8 | semidirect |
| 90. Dic37 | C4×Q8 | semidirect |
| 104. C37 | C4×C4⋊Q8 | semidirect |
| 109. C4⋊Q8 | #3866 | direct (N × H) |
| 187. C4 | Q8×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#3866 | 2 |
| (C2×#3866)⋊Q8 | 2 |
| #14558484 | 2 |
| #14558479 | 2 |
| C4⋊C4×#3866 | 2 |
| C42×#3866 | 2 |
| C4⋊Q8×D37 | 2 |
| C4×C4⋊Q8 | 37 |