Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C4×D4×D149 | C2 | semidirect |
| 4. #23749839 | C2 | semidirect |
| 5. #23749838 | C2 | semidirect |
| 6. #23749831 | C2 | semidirect |
| 7. #23749830 | C2 | semidirect |
| 8. #23749817 | C2 | semidirect |
| 9. #23749647 | C2 | semidirect |
| 10. #23749623 | C2 | semidirect |
| 11. #459×C149 | C2 | semidirect |
| 20. #18011911 | C22 | semidirect |
| 21. #18011898 | C22 | semidirect |
| 34. C4⋊#11924746 | C22 | semidirect |
| 35. #18011840 | C22 | semidirect |
| 36. #18011836 | C22 | semidirect |
| 37. #18011834 | C22 | semidirect |
| 38. #18011832 | C22 | semidirect |
| 40. #127×C149 | C22 | semidirect |
| 42. C4⋊C8×C149 | C22 | semidirect |
| 43. #102×C149 | C22 | semidirect |
| 52. D4×D149 | D4 | semidirect |
| 145. C4×C149 | AGL(1,ℤ/8) | semidirect |
| 160. C149 | #3036 | semidirect |
| 170. #459 | D149 | semidirect |
| 183. #127 | C2×D149 | semidirect |
| 200. C4⋊C8 | C2×D149 | semidirect |
| 204. #102 | C2×D149 | semidirect |
| 311. 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 |
| C4×D4×D149 | 2 |
| #23749839 | 2 |
| #23749838 | 2 |
| #23749831 | 2 |
| #23749830 | 2 |
| #23749817 | 2 |
| #23749647 | 2 |
| #23749623 | 2 |
| #459×C149 | 2 |
| #3036 | 149 |