Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #23752553 | C2 | semidirect |
| 3. #23752547 | C2 | semidirect |
| 4. #23752542 | C2 | semidirect |
| 5. #23752536 | C2 | semidirect |
| 6. #23752530 | C2 | semidirect |
| 7. #23752525 | C2 | semidirect |
| 8. #23752248 | C2 | semidirect |
| 9. #23752206 | C2 | semidirect |
| 10. C2×C22⋊(C151⋊C8) | C2 | semidirect |
| 11. C2×#117×C151 | C2 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012672 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. #18012670 | C22 | semidirect |
| 27. #18012662 | C22 | semidirect |
| 28. #18012662 | C22 | semidirect |
| 29. #18012659 | C22 | semidirect |
| 30. #18012659 | C22 | semidirect |
| 143. C151 | #3091 | semidirect |
| 146. C2×#117 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752723 | 2 |
| #23752553 | 2 |
| #23752547 | 2 |
| #23752542 | 2 |
| #23752536 | 2 |
| #23752530 | 2 |
| #23752525 | 2 |
| #23752248 | 2 |
| #23752206 | 2 |
| C2×C22⋊(C151⋊C8) | 2 |
| C2×#117×C151 | 2 |
| #3091 | 151 |