Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
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×#18012763 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. C4×D4×D151 | C2 | semidirect |
| 4. #23752426 | C2 | semidirect |
| 5. #23752425 | C2 | semidirect |
| 6. #23752418 | C2 | semidirect |
| 7. #23752417 | C2 | semidirect |
| 8. #23752404 | C2 | semidirect |
| 9. #23752234 | C2 | semidirect |
| 10. #23752210 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 20. #18012739 | C22 | semidirect |
| 21. #18012726 | C22 | semidirect |
| 34. C4⋊(C151⋊C8) | C22 | semidirect |
| 35. Dic151⋊C8 | C22 | semidirect |
| 36. #18012664 | C22 | semidirect |
| 37. #18012662 | C22 | semidirect |
| 38. #18012660 | C22 | semidirect |
| 40. #127×C151 | C22 | semidirect |
| 42. C4⋊C8×C151 | C22 | semidirect |
| 43. #102×C151 | C22 | semidirect |
| 52. D4×D151 | D4 | semidirect |
| 145. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 160. C151 | #3036 | semidirect |
| 170. #459 | D151 | semidirect |
| 183. #127 | C2×D151 | semidirect |
| 200. C4⋊C8 | C2×D151 | semidirect |
| 204. #102 | C2×D151 | semidirect |
| 311. C4 | #18012763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012763 | 2 |
| #23752760 | 2 |
| C4×D4×D151 | 2 |
| #23752426 | 2 |
| #23752425 | 2 |
| #23752418 | 2 |
| #23752417 | 2 |
| #23752404 | 2 |
| #23752234 | 2 |
| #23752210 | 2 |
| #459×C151 | 2 |
| #3036 | 151 |