Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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. #23750576 | C2 | semidirect |
| 3. #23750575 | C2 | semidirect |
| 4. #23750568 | C2 | semidirect |
| 5. #23750567 | C2 | semidirect |
| 6. C4×C4⋊#10597010 | C2 | semidirect |
| 7. #23750561 | C2 | semidirect |
| 22. C4×D596 | C4 | semidirect |
| 23. D4×Dic149 | C4 | semidirect |
| 24. #18011873 | C4 | semidirect |
| 25. C4×C22⋊D149 | C4 | semidirect |
| 26. #18011871 | C4 | semidirect |
| 30. C4×D4×C149 | C4 | semidirect |
| 132. C149 | #2319 | semidirect |
| 149. C4×D4 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750577 | 2 |
| #23750576 | 2 |
| #23750575 | 2 |
| #23750568 | 2 |
| #23750567 | 2 |
| C4×C4⋊#10597010 | 2 |
| #23750561 | 2 |
| C4×D4×D149 | 2 |
| #2319 | 149 |