Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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×#18012765 | C2 | semidirect |
| 2. C22×#14558989 | C2 | semidirect |
| 3. #23752781 | C2 | semidirect |
| 4. #23752427 | C2 | semidirect |
| 5. #23752407 | C2 | semidirect |
| 6. #23752239 | C2 | semidirect |
| 7. #23752216 | C2 | semidirect |
| 8. #23752206 | C2 | semidirect |
| 9. #518×C151 | C2 | semidirect |
| 13. C2×#14558992 | C22 | semidirect |
| 16. C2×#14558989 | C22 | semidirect |
| 19. #18012736 | C22 | semidirect |
| 20. #18012727 | C22 | semidirect |
| 23. C4⋊(C151⋊C8) | C22 | semidirect |
| 24. #18012662 | C22 | semidirect |
| 25. #18012659 | C22 | semidirect |
| 26. #18012659 | C22 | semidirect |
| 29. C4×D4×C151 | C22 | semidirect |
| 56. C2×D4×C151 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 126. #518 | D151 | semidirect |
| 147. C4×D4 | C2×D151 | semidirect |
| 169. C2×D4 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| C22×#14558989 | 2 |
| #23752781 | 2 |
| #23752427 | 2 |
| #23752407 | 2 |
| #23752239 | 2 |
| #23752216 | 2 |
| #23752206 | 2 |
| #518×C151 | 2 |
| #3041 | 151 |