Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D37 | C2 | semidirect |
| 3. #14557771 | C2 | semidirect |
| 4. #14557740 | C2 | semidirect |
| 5. #14557687 | C2 | semidirect |
| 6. C4×Dic148 | C2 | semidirect |
| 8. C37×#494 | C2 | semidirect |
| 53. Dic148 | D4 | semidirect |
| 65. D148 | Q16 | semidirect |
| 78. C2×D37 | C2×Q16 | semidirect |
| 81. C4×C37 | C2×Q16 | semidirect |
| 94. #494 | D37 | semidirect |
| 100. C37 | D4×Q16 | semidirect |
| 176. C4 | Q16×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| #14558198 | 2 |
| #14557771 | 2 |
| #14557740 | 2 |
| #14557687 | 2 |
| C4×Dic148 | 2 |
| C8×D148 | 2 |
| C37×#494 | 2 |
| D4×Q16 | 37 |