Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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×#18012718 | C2 | semidirect |
| 3. #23752548 | C2 | semidirect |
| 4. #23752526 | C2 | semidirect |
| 5. #23752458 | C2 | semidirect |
| 6. #23752365 | C2 | semidirect |
| 7. #23752353 | C2 | semidirect |
| 8. #407×C151 | C2 | semidirect |
| 9. C22×Dic302 | C22 | semidirect |
| 12. C2×#14558993 | C22 | semidirect |
| 16. #18012718 | C22 | semidirect |
| 22. C2×C4⋊Dic151 | C22 | semidirect |
| 26. #18012673 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 28. #18012661 | C22 | semidirect |
| 30. C2×M16×C151 | C22 | semidirect |
| 32. C22⋊C8×C151 | C22 | semidirect |
| 129. C151 | #3193 | semidirect |
| 138. #407 | D151 | semidirect |
| 144. C2×M16 | C2×D151 | semidirect |
| 162. C22⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012718 | 2 |
| C2×#18012713 | 2 |
| #23752548 | 2 |
| #23752526 | 2 |
| #23752458 | 2 |
| #23752365 | 2 |
| #23752353 | 2 |
| #407×C151 | 2 |
| #3193 | 151 |