Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#11924556 | C2 | semidirect |
| 2. #14558188 | C2 | semidirect |
| 3. #14557905 | C2 | semidirect |
| 4. #14557760 | C2 | semidirect |
| 5. #14557743 | C2 | semidirect |
| 6. #14557725 | C2 | semidirect |
| 7. #14557695 | C2 | semidirect |
| 8. #14557676 | C2 | semidirect |
| 9. C4×#10596941 | C2 | semidirect |
| 10. D4×#64436 | C2 | semidirect |
| 11. C37×#550 | C2 | semidirect |
| 69. #10596941 | D4 | semidirect |
| 129. C4×C37 | #135 | semidirect |
| 142. #550 | D37 | semidirect |
| 152. C37 | #3284 | semidirect |
| 272. C4 | #11924556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924556 | 2 |
| #14558188 | 2 |
| #14557905 | 2 |
| #14557760 | 2 |
| #14557743 | 2 |
| #14557725 | 2 |
| #14557695 | 2 |
| #14557676 | 2 |
| C4×#10596941 | 2 |
| D4×#64436 | 2 |
| C37×#550 | 2 |
| #3284 | 37 |