Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#18012786 | C2 | semidirect |
| 2. C22×#14558992 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752354 | C2 | semidirect |
| 5. #23752349 | C2 | semidirect |
| 6. #23752222 | C2 | semidirect |
| 7. #23752208 | C2 | semidirect |
| 8. #23752180 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 15. C2×#14559003 | C22 | semidirect |
| 18. C2×Q8×D151 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 28. #18012663 | C22 | semidirect |
| 29. #18012660 | C22 | semidirect |
| 30. (C2×D151)⋊C8 | C22 | semidirect |
| 48. C2×Dic302 | D4 | semidirect |
| 69. #41×C151 | D4 | semidirect |
| 145. C151 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 191. #41 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012786 | 2 |
| C22×#14558992 | 2 |
| #23752779 | 2 |
| #23752354 | 2 |
| #23752349 | 2 |
| #23752222 | 2 |
| #23752208 | 2 |
| #23752180 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3010 | 151 |