Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18012736 | C2 | semidirect |
| 2. #23752602 | C2 | semidirect |
| 3. #23752578 | C2 | semidirect |
| 4. #23752412 | C2 | semidirect |
| 5. #23752407 | C2 | semidirect |
| 6. #23752362 | C2 | semidirect |
| 7. #23752345 | C2 | semidirect |
| 8. #23752269 | C2 | semidirect |
| 9. #529×C151 | C2 | semidirect |
| 13. C2×#14558991 | C22 | semidirect |
| 14. C2×#14558989 | C22 | semidirect |
| 19. C4⋊(C151⋊C8) | C22 | semidirect |
| 20. #18012659 | C22 | semidirect |
| 21. #18012659 | C22 | semidirect |
| 23. #18012650 | C22 | semidirect |
| 25. #125×C151 | C22 | semidirect |
| 26. #124×C151 | C22 | semidirect |
| 30. C4×Q8×C151 | C22 | semidirect |
| 32. C4×D4×C151 | C22 | semidirect |
| 127. C151 | #3217 | semidirect |
| 130. #529 | D151 | semidirect |
| 148. #125 | C2×D151 | semidirect |
| 149. #124 | C2×D151 | semidirect |
| 153. C4×Q8 | C2×D151 | semidirect |
| 155. C4×D4 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012736 | 2 |
| #23752602 | 2 |
| #23752578 | 2 |
| #23752412 | 2 |
| #23752407 | 2 |
| #23752362 | 2 |
| #23752345 | 2 |
| #23752269 | 2 |
| #529×C151 | 2 |
| #3217 | 151 |