Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #14557968 | C2 | semidirect |
| 2. #14557910 | C2 | semidirect |
| 3. #14557354 | C2 | semidirect |
| 4. #14557345 | C2 | semidirect |
| 5. C37×#443 | C2 | semidirect |
| 20. Q16×C37 | D4 | semidirect |
| 22. D8×C37 | D4 | semidirect |
| 64. #443 | D37 | semidirect |
| 67. C37 | #2213 | semidirect |
| 82. Q16 | D148 | semidirect |
| 88. D8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557968 | 2 |
| #14557910 | 2 |
| #14557354 | 2 |
| #14557345 | 2 |
| C37×#443 | 2 |
| #2213 | 37 |