Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D148 | C2 | semidirect |
| 2. #14557879 | C2 | semidirect |
| 3. #14557813 | C2 | semidirect |
| 4. #14557725 | C2 | semidirect |
| 5. Q8×#64436 | C2 | semidirect |
| 6. C4×#10596939 | C2 | semidirect |
| 7. C37×#550 | C2 | semidirect |
| 46. Q8×C37 | D8 | semidirect |
| 58. D148 | #41 | semidirect |
| 82. #550 | D37 | semidirect |
| 89. C37 | #3358 | semidirect |
| 129. Q8 | #10596939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D148 | 2 |
| #14557879 | 2 |
| #14557813 | 2 |
| #14557725 | 2 |
| Q8×#64436 | 2 |
| C4×#10596939 | 2 |
| C37×#550 | 2 |
| #3358 | 37 |