Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18011935 | C2 | semidirect |
| 2. #23750173 | C2 | semidirect |
| 3. #127×D149 | C2 | semidirect |
| 4. #23750013 | C2 | semidirect |
| 5. #23750001 | C2 | semidirect |
| 6. #23749998 | C2 | semidirect |
| 7. #23749997 | C2 | semidirect |
| 8. C4×#14558719 | C2 | semidirect |
| 9. #493×C149 | C2 | semidirect |
| 14. C2×#14558725 | C22 | semidirect |
| 15. C2×#14558724 | C22 | semidirect |
| 16. C2×#14558721 | C22 | semidirect |
| 18. #18011911 | C22 | semidirect |
| 22. #18011898 | C22 | semidirect |
| 26. #18011821 | C22 | semidirect |
| 27. C4×#11924746 | C22 | semidirect |
| 28. C2×D8×C149 | C22 | semidirect |
| 30. #127×C149 | C22 | semidirect |
| 31. C4×C8×C149 | C22 | semidirect |
| 48. #14558719 | D4 | semidirect |
| 77. #11924746 | C2×D4 | semidirect |
| 86. C8×C149 | C2×D4 | semidirect |
| 97. C4×C149 | AGL(1,ℤ/8) | semidirect |
| 108. C149 | #3151 | semidirect |
| 115. #493 | D149 | semidirect |
| 126. C2×D8 | C2×D149 | semidirect |
| 133. #127 | C2×D149 | semidirect |
| 140. C4×C8 | C2×D149 | semidirect |
| 195. C8 | D4×D149 | semidirect |
| 209. C4 | #18011935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011935 | 2 |
| #23750173 | 2 |
| #127×D149 | 2 |
| #23750013 | 2 |
| #23750001 | 2 |
| #23749998 | 2 |
| #23749997 | 2 |
| C4×#14558719 | 2 |
| #493×C149 | 2 |
| #3151 | 149 |