Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11924567 | C2 | semidirect |
| 3. #14557755 | C2 | semidirect |
| 4. #14557743 | C2 | semidirect |
| 5. #14557733 | C2 | semidirect |
| 6. #14557557 | C2 | semidirect |
| 7. #14557532 | C2 | semidirect |
| 8. C2×C4×Q8×C37 | C2 | semidirect |
| 36. C2×Q8×C37 | D4 | semidirect |
| 111. C4×C37 | #137 | semidirect |
| 123. C2×C4×Q8 | D37 | semidirect |
| 129. C37 | #3037 | semidirect |
| 160. C2×Q8 | D148 | semidirect |
| 233. C4 | #11924567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924567 | 2 |
| #14558083 | 2 |
| #14557755 | 2 |
| #14557743 | 2 |
| #14557733 | 2 |
| #14557557 | 2 |
| #14557532 | 2 |
| C2×C4×Q8×C37 | 2 |
| #3037 | 37 |