Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558253 | C2 | semidirect |
| 2. D4×Dic74 | C2 | semidirect |
| 3. #14557891 | C2 | semidirect |
| 4. #14557884 | C2 | semidirect |
| 5. #14557827 | C2 | semidirect |
| 6. #14557813 | C2 | semidirect |
| 8. #14557738 | C2 | semidirect |
| 9. #14557663 | C2 | semidirect |
| 10. #14557630 | C2 | semidirect |
| 134. C37 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558253 | 2 |
| D4×Dic74 | 2 |
| #14557891 | 2 |
| #14557884 | 2 |
| #14557827 | 2 |
| #14557813 | 2 |
| #14557746 | 2 |
| #14557738 | 2 |
| #14557663 | 2 |
| #14557630 | 2 |
| C4×D8×C37 | 2 |
| #3367 | 37 |