Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #23750590 | C2 | semidirect |
| 4. C2×C8×#10597010 | C2 | semidirect |
| 5. #23750501 | C2 | semidirect |
| 6. #23750495 | C2 | semidirect |
| 9. #18011999 | C4 | semidirect |
| 16. #18011976 | C4 | semidirect |
| 23. #18011835 | C4 | semidirect |
| 24. #18011833 | C4 | semidirect |
| 25. #18011831 | C4 | semidirect |
| 26. #103×C149 | C4 | semidirect |
| 109. C149 | #1764 | semidirect |
| 131. #103 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011999 | 2 |
| C2×#18011976 | 2 |
| #23750590 | 2 |
| C2×C8×#10597010 | 2 |
| #23750501 | 2 |
| #23750495 | 2 |
| #23749620 | 2 |
| #1764 | 149 |