Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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. #23750584 | C2 | semidirect |
| 3. C4×C4⋊#10597010 | C2 | semidirect |
| 4. #23750498 | C2 | semidirect |
| 9. #18011973 | C4 | semidirect |
| 15. C4×D596 | C4 | semidirect |
| 16. D4×Dic149 | C4 | semidirect |
| 17. #18011873 | C4 | semidirect |
| 23. C4×D4×C149 | C4 | semidirect |
| 26. D149⋊C8 | C2×C4 | semidirect |
| 29. C4⋊#10597010 | C2×C4 | semidirect |
| 68. D596 | C42 | semidirect |
| 85. D4×C149 | C42 | semidirect |
| 121. C149 | #1762 | semidirect |
| 136. C4×D4 | #10597010 | semidirect |
| 190. D4 | C4×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011973 | 2 |
| #23750584 | 2 |
| C4×C4⋊#10597010 | 2 |
| #23750498 | 2 |
| C4×D4×D149 | 2 |
| #1762 | 149 |