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. #23749959 | C2 | semidirect |
| 4. #23749958 | C2 | semidirect |
| 5. #23749918 | C2 | semidirect |
| 6. #23749863 | C2 | semidirect |
| 7. Q16×Dic149 | C2 | semidirect |
| 9. C2×#18011845 | C2 | semidirect |
| 10. #107×D149 | C2 | semidirect |
| 11. #467×C149 | C2 | semidirect |
| 71. C22⋊D149 | Q16 | semidirect |
| 116. C149 | #3338 | semidirect |
| 124. #467 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750333 | 2 |
| #23750029 | 2 |
| #23749959 | 2 |
| #23749958 | 2 |
| #23749918 | 2 |
| #23749863 | 2 |
| Q16×Dic149 | 2 |
| C8×C22⋊D149 | 2 |
| C2×#18011845 | 2 |
| #107×D149 | 2 |
| #467×C149 | 2 |
| #3338 | 149 |