Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 2. #14557657 | C2 | direct (N × H) |
| 26. C2×Dic74 | C8 | semidirect |
| 37. C2×#64436 | Q8 | semidirect |
| 53. Dic74 | C2×C8 | semidirect |
| 56. #64436 | C2×Q8 | semidirect |
| 69. C2×C37 | C8×Q8 | semidirect |
| 79. C37 | C2×C8×Q8 | semidirect |
| 141. C2 | #14557657 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic74 | 2 |
| #14557657 | 2 |
| C2×#11924465 | 2 |
| C2×C4×#64436 | 2 |
| C2×C8×Dic37 | 2 |
| C2×C4⋊C8×C37 | 2 |
| C2×C8×Q8 | 37 |