Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #23750348 | C2 | semidirect |
| 3. #23749972 | C2 | semidirect |
| 4. #23749952 | C2 | semidirect |
| 5. #23749910 | C2 | semidirect |
| 6. #23749857 | C2 | semidirect |
| 7. #23749825 | C2 | semidirect |
| 8. #23749786 | C2 | semidirect |
| 9. C8×D596 | C2 | semidirect |
| 10. #23749620 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 127. C149 | #3304 | semidirect |
| 137. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750348 | 2 |
| #23750297 | 2 |
| #23749972 | 2 |
| #23749952 | 2 |
| #23749910 | 2 |
| #23749857 | 2 |
| #23749825 | 2 |
| #23749786 | 2 |
| C8×D596 | 2 |
| #23749620 | 2 |
| C4×Q16×C149 | 2 |
| #3304 | 149 |