Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 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 |
|---|---|---|
| 1. C2×#18011937 | C2 | semidirect |
| 2. #23750175 | C2 | semidirect |
| 3. #23750012 | C2 | semidirect |
| 4. #23750001 | C2 | semidirect |
| 5. #23749997 | C2 | semidirect |
| 6. C4×#14558720 | C2 | semidirect |
| 7. C2×#127×C149 | C2 | semidirect |
| 10. C2×#14558724 | C22 | semidirect |
| 11. C2×#14558721 | C22 | semidirect |
| 13. #18011911 | C22 | semidirect |
| 14. #18011908 | C22 | semidirect |
| 15. #18011899 | C22 | semidirect |
| 18. #18011822 | C22 | semidirect |
| 19. C4×#11924746 | C22 | semidirect |
| 34. #14558720 | D4 | semidirect |
| 57. #11924746 | C2×D4 | semidirect |
| 82. C4×C149 | AGL(1,ℤ/8) | semidirect |
| 90. C149 | #3151 | semidirect |
| 94. C2×#127 | D149 | semidirect |
| 174. C4 | #18011937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011937 | 2 |
| #23750175 | 2 |
| #23750012 | 2 |
| #23750001 | 2 |
| #23749997 | 2 |
| C4×#14558720 | 2 |
| C2×#127×C149 | 2 |
| #3151 | 149 |