Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#18011982 | C2 | semidirect |
| 3. #23750632 | C2 | semidirect |
| 5. #23750495 | C2 | semidirect |
| 6. (C2×#10597010)⋊C8 | C2 | semidirect |
| 23. #18011836 | C4 | semidirect |
| 24. #18011834 | C4 | semidirect |
| 25. #18011832 | C4 | semidirect |
| 26. #102×C149 | C4 | semidirect |
| 109. C149 | #1866 | semidirect |
| 136. #102 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011998 | 2 |
| C2×#18011982 | 2 |
| #23750632 | 2 |
| C2×#18011975 | 2 |
| #23750495 | 2 |
| (C2×#10597010)⋊C8 | 2 |
| #23749618 | 2 |
| #1866 | 149 |