Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 1. C2×#18011919 | C2 | semidirect |
| 2. C22×#14558719 | C2 | semidirect |
| 4. #23749702 | C2 | semidirect |
| 5. #23749695 | C2 | semidirect |
| 6. #23749591 | C2 | semidirect |
| 7. #23749588 | C2 | semidirect |
| 8. #23749581 | C2 | semidirect |
| 9. #424×C149 | C2 | semidirect |
| 17. C2×#14558719 | C22 | semidirect |
| 19. C2×C8×D149 | C22 | semidirect |
| 26. #18011823 | C22 | semidirect |
| 27. #18011822 | C22 | semidirect |
| 28. C4×#11924746 | C22 | semidirect |
| 32. C4⋊C8×C149 | C22 | semidirect |
| 50. C2×#11924746 | D4 | semidirect |
| 113. C149 | #2930 | semidirect |
| 120. #424 | D149 | semidirect |
| 142. C4⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011919 | 2 |
| C22×#14558719 | 2 |
| #23750137 | 2 |
| #23749702 | 2 |
| #23749695 | 2 |
| #23749591 | 2 |
| #23749588 | 2 |
| #23749581 | 2 |
| #424×C149 | 2 |
| #2930 | 149 |