Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
| 2. C2×#11924481 | C2 | semidirect |
| 3. C2×#11924479 | C2 | semidirect |
| 5. #14557336 | C2 | semidirect |
| 6. #14557312 | C2 | semidirect |
| 7. C37×#358 | C2 | semidirect |
| 33. Q16×C37 | D4 | semidirect |
| 40. Dic148 | D4 | semidirect |
| 74. C2×D37 | SD32 | semidirect |
| 92. #358 | D37 | semidirect |
| 94. C37 | #2185 | semidirect |
| 123. Q16 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| C2×#11924481 | 2 |
| C2×#11924479 | 2 |
| #14557770 | 2 |
| #14557336 | 2 |
| #14557312 | 2 |
| C37×#358 | 2 |
| #2185 | 37 |