Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#18012747 | C2 | semidirect |
| 2. C22×C8×D151 | C2 | semidirect |
| 4. #23752282 | C2 | semidirect |
| 5. #23752277 | C2 | semidirect |
| 6. #23752178 | C2 | semidirect |
| 7. #23752175 | C2 | semidirect |
| 8. #23752168 | C2 | semidirect |
| 9. #424×C151 | C2 | semidirect |
| 14. C2×#14558987 | C22 | semidirect |
| 19. C2×C8×D151 | C22 | semidirect |
| 26. (C2×D151)⋊C8 | C22 | semidirect |
| 27. #18012650 | C22 | semidirect |
| 28. C4×C151⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C151 | C22 | semidirect |
| 48. C2×C151⋊C8 | D4 | semidirect |
| 101. C2×D151 | #131 | semidirect |
| 113. C151 | #2929 | semidirect |
| 120. #424 | D151 | semidirect |
| 142. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012747 | 2 |
| C22×C8×D151 | 2 |
| #23752724 | 2 |
| #23752282 | 2 |
| #23752277 | 2 |
| #23752178 | 2 |
| #23752175 | 2 |
| #23752168 | 2 |
| #424×C151 | 2 |
| #2929 | 151 |