Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. #23750159 | C2 | semidirect |
| 2. C2×#18011899 | C2 | semidirect |
| 3. #23750009 | C2 | semidirect |
| 4. #23749980 | C2 | semidirect |
| 5. #23749848 | C2 | semidirect |
| 6. #23749841 | C2 | semidirect |
| 7. #23749783 | C2 | semidirect |
| 8. #23749778 | C2 | semidirect |
| 9. #23749766 | C2 | semidirect |
| 11. #431×C149 | C2 | semidirect |
| 14. C2×Dic596 | C22 | semidirect |
| 16. C2×#14558725 | C22 | semidirect |
| 19. #18011903 | C22 | semidirect |
| 24. #18011899 | C22 | semidirect |
| 28. C4×Dic298 | C22 | semidirect |
| 29. C4×D596 | C22 | semidirect |
| 34. #18011836 | C22 | semidirect |
| 35. #18011836 | C22 | semidirect |
| 39. C4⋊C8×C149 | C22 | semidirect |
| 42. C4×C8×C149 | C22 | semidirect |
| 143. C149 | #3211 | semidirect |
| 155. #431 | D149 | semidirect |
| 179. C4⋊C8 | C2×D149 | semidirect |
| 186. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750159 | 2 |
| C2×#18011899 | 2 |
| #23750009 | 2 |
| #23749980 | 2 |
| #23749848 | 2 |
| #23749841 | 2 |
| #23749783 | 2 |
| #23749778 | 2 |
| #23749766 | 2 |
| #23749761 | 2 |
| #431×C149 | 2 |
| #3211 | 149 |