Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012767 | C2 | semidirect |
| 2. #23752790 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752465 | C2 | semidirect |
| 5. #23752458 | C2 | semidirect |
| 6. #23752448 | C2 | semidirect |
| 7. #23752441 | C2 | semidirect |
| 8. #23752254 | C2 | semidirect |
| 9. #23752209 | C2 | semidirect |
| 10. C2×#18012661 | C2 | semidirect |
| 11. C2×#131×C151 | C2 | semidirect |
| 19. #18012718 | C22 | semidirect |
| 23. #18012713 | C22 | semidirect |
| 29. #18012673 | C22 | semidirect |
| 30. #18012671 | C22 | semidirect |
| 31. #18012664 | C22 | semidirect |
| 32. #18012664 | C22 | semidirect |
| 35. #18012661 | C22 | semidirect |
| 36. #18012661 | C22 | semidirect |
| 40. C2×M16×C151 | C22 | semidirect |
| 42. C22×C8×C151 | C22 | semidirect |
| 79. M16×C151 | D4 | semidirect |
| 151. C151 | #3062 | semidirect |
| 154. C2×#131 | D151 | semidirect |
| 172. C2×M16 | C2×D151 | semidirect |
| 174. C22×C8 | C2×D151 | semidirect |
| 220. M16 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| #23752790 | 2 |
| #23752776 | 2 |
| #23752465 | 2 |
| #23752458 | 2 |
| #23752448 | 2 |
| #23752441 | 2 |
| #23752254 | 2 |
| #23752209 | 2 |
| C2×#18012661 | 2 |
| C2×#131×C151 | 2 |
| #3062 | 151 |