Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750017 | C2 | semidirect |
| 3. #23749987 | C2 | semidirect |
| 4. #23749847 | C2 | semidirect |
| 5. #23749780 | C2 | semidirect |
| 7. #23749682 | C2 | semidirect |
| 8. #533×C149 | C2 | semidirect |
| 11. C2×#14558726 | C22 | semidirect |
| 19. C4⋊#11924746 | C22 | semidirect |
| 20. #18011834 | C22 | semidirect |
| 23. #18011822 | C22 | semidirect |
| 24. C4⋊Q8×C149 | C22 | semidirect |
| 25. C4⋊Q8×C149 | C22 | semidirect |
| 30. C4×Q8×C149 | C22 | semidirect |
| 112. C149 | #3215 | semidirect |
| 114. #533 | D149 | semidirect |
| 126. C4⋊Q8 | C2×D149 | semidirect |
| 127. C4⋊Q8 | C2×D149 | semidirect |
| 136. C4×Q8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011899 | 2 |
| #23750017 | 2 |
| #23749987 | 2 |
| #23749847 | 2 |
| #23749780 | 2 |
| #23749775 | 2 |
| #23749682 | 2 |
| #533×C149 | 2 |
| #3215 | 149 |