Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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. #14558164 | C2 | direct (N × H) |
| 2. C2×#11924535 | C2 | semidirect |
| 3. C2×#11924527 | C2 | semidirect |
| 8. #11924535 | C22 | semidirect |
| 9. #11924527 | C22 | semidirect |
| 24. C22×C4×C37 | Q8 | semidirect |
| 48. C2×C4×C37 | C2×Q8 | semidirect |
| 70. C2×C37 | #544 | semidirect |
| 80. C37 | C2×#544 | semidirect |
| 102. C22×C4 | Dic74 | semidirect |
| 127. C2×C4 | C2×Dic74 | semidirect |
| 143. C2 | #14558164 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558164 | 2 |
| C2×#11924535 | 2 |
| C2×#11924527 | 2 |
| C2×#11924515 | 2 |
| C2×#11924495 | 2 |
| C22×C4⋊C4×C37 | 2 |
| C2×#544 | 37 |