Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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. #23750574 | C2 | semidirect |
| 3. C4×C4⋊#10597010 | C2 | semidirect |
| 5. #23750561 | C2 | semidirect |
| 6. C42×#10597010 | C2 | semidirect |
| 17. #18011870 | C4 | semidirect |
| 18. #18011869 | C4 | semidirect |
| 19. #18011868 | C4 | semidirect |
| 20. #18011868 | C4 | semidirect |
| 21. #18011867 | C4 | semidirect |
| 26. #117×C149 | C4 | semidirect |
| 108. C149 | #2298 | semidirect |
| 123. #117 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750575 | 2 |
| #23750574 | 2 |
| C4×C4⋊#10597010 | 2 |
| C4×C22⋊#10597010 | 2 |
| #23750561 | 2 |
| C42×#10597010 | 2 |
| #117×D149 | 2 |
| #2298 | 149 |