Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11924557 | C2 | semidirect |
| 2. #14558205 | C2 | semidirect |
| 3. #14558203 | C2 | semidirect |
| 4. #14557909 | C2 | semidirect |
| 5. #14557768 | C2 | semidirect |
| 6. #14557734 | C2 | semidirect |
| 7. #14557679 | C2 | semidirect |
| 8. #14557677 | C2 | semidirect |
| 9. C4×#10596942 | C2 | semidirect |
| 10. #14557598 | C2 | semidirect |
| 11. C37×#460 | C2 | semidirect |
| 69. #10596942 | D4 | semidirect |
| 130. C4×C37 | #135 | semidirect |
| 149. #460 | D37 | semidirect |
| 154. C37 | #3287 | semidirect |
| 276. C4 | #11924557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924557 | 2 |
| #14558205 | 2 |
| #14558203 | 2 |
| #14557909 | 2 |
| #14557768 | 2 |
| #14557734 | 2 |
| #14557679 | 2 |
| #14557677 | 2 |
| C4×#10596942 | 2 |
| #14557598 | 2 |
| C37×#460 | 2 |
| #3287 | 37 |