Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 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. #23749704 | C2 | semidirect |
| 3. #23749702 | C2 | semidirect |
| 4. #23749698 | C2 | semidirect |
| 5. #23749695 | C2 | semidirect |
| 6. #23749686 | C2 | semidirect |
| 7. #23749590 | C2 | semidirect |
| 8. #23749587 | C2 | semidirect |
| 9. #433×C149 | C2 | semidirect |
| 14. C2×#14558719 | C22 | semidirect |
| 15. C2×C8×D149 | C22 | semidirect |
| 22. C4⋊#11924746 | C22 | semidirect |
| 26. #18011823 | C22 | semidirect |
| 27. #18011823 | C22 | semidirect |
| 28. #18011822 | C22 | semidirect |
| 29. C4×#11924746 | C22 | semidirect |
| 31. C4⋊C8×C149 | C22 | semidirect |
| 33. #97×C149 | C22 | semidirect |
| 34. C4×C8×C149 | C22 | semidirect |
| 114. C149 | #2978 | semidirect |
| 122. #433 | D149 | semidirect |
| 139. C4⋊C8 | C2×D149 | semidirect |
| 147. #97 | C2×D149 | semidirect |
| 149. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750137 | 2 |
| #23749704 | 2 |
| #23749702 | 2 |
| #23749698 | 2 |
| #23749695 | 2 |
| #23749686 | 2 |
| #23749590 | 2 |
| #23749587 | 2 |
| #433×C149 | 2 |
| #2978 | 149 |