Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #23750028 | C2 | semidirect |
| 4. #23749962 | C2 | semidirect |
| 5. #23749959 | C2 | semidirect |
| 6. #23749921 | C2 | semidirect |
| 7. #23749865 | C2 | semidirect |
| 8. C4×#14558726 | C2 | semidirect |
| 10. #107×D149 | C2 | semidirect |
| 11. #477×C149 | C2 | semidirect |
| 77. D596 | Q16 | semidirect |
| 117. C149 | #3338 | semidirect |
| 125. #477 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750336 | 2 |
| #23750335 | 2 |
| #23750028 | 2 |
| #23749962 | 2 |
| #23749959 | 2 |
| #23749921 | 2 |
| #23749865 | 2 |
| C4×#14558726 | 2 |
| #23749690 | 2 |
| #107×D149 | 2 |
| #477×C149 | 2 |
| #3338 | 149 |