Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#18011891 | C2 | semidirect |
| 3. #23749969 | C2 | semidirect |
| 4. #23749938 | C2 | semidirect |
| 5. #23749865 | C2 | semidirect |
| 6. #23749855 | C2 | semidirect |
| 7. #23749790 | C2 | semidirect |
| 8. #23749780 | C2 | semidirect |
| 9. #23749766 | C2 | semidirect |
| 10. C22⋊C8×D149 | C2 | semidirect |
| 11. #483×C149 | C2 | semidirect |
| 15. C2×#14558726 | C22 | semidirect |
| 16. C2×#14558725 | C22 | semidirect |
| 32. #18011844 | C22 | semidirect |
| 33. #18011836 | C22 | semidirect |
| 34. #18011834 | C22 | semidirect |
| 35. #18011831 | C22 | semidirect |
| 40. #106×C149 | C22 | semidirect |
| 41. #103×C149 | C22 | semidirect |
| 149. C149 | #3190 | semidirect |
| 154. #483 | D149 | semidirect |
| 185. #106 | C2×D149 | semidirect |
| 188. #103 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750138 | 2 |
| C2×#18011891 | 2 |
| #23749969 | 2 |
| #23749938 | 2 |
| #23749865 | 2 |
| #23749855 | 2 |
| #23749790 | 2 |
| #23749780 | 2 |
| #23749766 | 2 |
| C22⋊C8×D149 | 2 |
| #483×C149 | 2 |
| #3190 | 149 |