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. #23752746 | C2 | semidirect |
| 3. #23752601 | C2 | semidirect |
| 4. #23752577 | C2 | semidirect |
| 5. #23752413 | C2 | semidirect |
| 6. #23752408 | C2 | semidirect |
| 7. #23752365 | C2 | semidirect |
| 8. #23752348 | C2 | semidirect |
| 9. #432×C151 | C2 | semidirect |
| 13. C2×#14558993 | C22 | semidirect |
| 14. C2×D1208 | C22 | semidirect |
| 20. #18012731 | C22 | semidirect |
| 21. #18012727 | C22 | semidirect |
| 25. C4×Dic302 | C22 | semidirect |
| 26. C4×D604 | C22 | semidirect |
| 29. #18012661 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 32. C4⋊C8×C151 | C22 | semidirect |
| 34. #97×C151 | C22 | semidirect |
| 127. C151 | #3217 | semidirect |
| 137. #432 | D151 | semidirect |
| 158. C4⋊C8 | C2×D151 | semidirect |
| 162. #97 | 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 |
| #23752746 | 2 |
| #23752601 | 2 |
| #23752577 | 2 |
| #23752413 | 2 |
| #23752408 | 2 |
| #23752365 | 2 |
| #23752348 | 2 |
| #432×C151 | 2 |
| #3217 | 151 |