Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
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×#18012763 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. #127×D151 | C2 | semidirect |
| 4. #23752600 | C2 | semidirect |
| 5. #23752588 | C2 | semidirect |
| 6. #23752585 | C2 | semidirect |
| 7. #23752584 | C2 | semidirect |
| 8. C4×#14558987 | C2 | semidirect |
| 9. #493×C151 | C2 | semidirect |
| 14. C2×#14558993 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 16. C2×#14558989 | C22 | semidirect |
| 18. #18012739 | C22 | semidirect |
| 22. #18012726 | C22 | semidirect |
| 26. #18012649 | C22 | semidirect |
| 27. C4×C151⋊C8 | C22 | semidirect |
| 28. C2×D8×C151 | C22 | semidirect |
| 30. #127×C151 | C22 | semidirect |
| 31. C4×C8×C151 | C22 | semidirect |
| 48. #14558987 | D4 | semidirect |
| 77. C151⋊C8 | C2×D4 | semidirect |
| 86. C8×C151 | C2×D4 | semidirect |
| 97. C4×C151 | AGL(1,ℤ/8) | semidirect |
| 108. C151 | #3151 | semidirect |
| 115. #493 | D151 | semidirect |
| 126. C2×D8 | C2×D151 | semidirect |
| 133. #127 | C2×D151 | semidirect |
| 140. C4×C8 | C2×D151 | semidirect |
| 195. C8 | D4×D151 | semidirect |
| 209. 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 |
| #127×D151 | 2 |
| #23752600 | 2 |
| #23752588 | 2 |
| #23752585 | 2 |
| #23752584 | 2 |
| C4×#14558987 | 2 |
| #493×C151 | 2 |
| #3151 | 151 |