Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #23750632 | C2 | semidirect |
| 4. C2×C8×#10597010 | C2 | semidirect |
| 5. #23750501 | C2 | semidirect |
| 6. #23750495 | C2 | semidirect |
| 21. #18011835 | C4 | semidirect |
| 22. #18011833 | C4 | semidirect |
| 23. #18011831 | C4 | semidirect |
| 24. #103×C149 | C4 | semidirect |
| 105. C149 | #1937 | semidirect |
| 125. #103 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750632 | 2 |
| C2×#18011976 | 2 |
| #23750600 | 2 |
| C2×C8×#10597010 | 2 |
| #23750501 | 2 |
| #23750495 | 2 |
| #23749620 | 2 |
| #1937 | 149 |