Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #23750029 | C2 | semidirect |
| 3. #23749962 | C2 | semidirect |
| 4. #23749960 | C2 | semidirect |
| 5. #23749919 | C2 | semidirect |
| 6. #23749867 | C2 | semidirect |
| 7. #23749866 | C2 | semidirect |
| 8. #23749719 | C2 | semidirect |
| 10. #107×D149 | C2 | semidirect |
| 11. C2×#107×C149 | C2 | semidirect |
| 73. C22⋊D149 | Q16 | semidirect |
| 116. C149 | #3338 | semidirect |
| 128. C2×#107 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750330 | 2 |
| #23750029 | 2 |
| #23749962 | 2 |
| #23749960 | 2 |
| #23749919 | 2 |
| #23749867 | 2 |
| #23749866 | 2 |
| #23749719 | 2 |
| C8×C22⋊D149 | 2 |
| #107×D149 | 2 |
| C2×#107×C149 | 2 |
| #3338 | 149 |