Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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. #23750361 | C2 | semidirect |
| 2. D4×Dic298 | C2 | semidirect |
| 3. #23749983 | C2 | semidirect |
| 4. #23749971 | C2 | semidirect |
| 5. #23749913 | C2 | semidirect |
| 6. #23749911 | C2 | semidirect |
| 7. #23749838 | C2 | semidirect |
| 8. #23749752 | C2 | semidirect |
| 9. #23749737 | C2 | semidirect |
| 10. C4×#14558724 | C2 | semidirect |
| 124. C149 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750361 | 2 |
| D4×Dic298 | 2 |
| #23749983 | 2 |
| #23749971 | 2 |
| #23749913 | 2 |
| #23749911 | 2 |
| #23749838 | 2 |
| #23749752 | 2 |
| #23749737 | 2 |
| C4×#14558724 | 2 |
| #459×C149 | 2 |
| #3373 | 149 |