Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752536 | C2 | semidirect |
| 3. #23752536 | C2 | semidirect |
| 4. #23752530 | C2 | semidirect |
| 5. #23752525 | C2 | semidirect |
| 6. #23752252 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752216 | C2 | semidirect |
| 9. C2×#18012659 | C2 | semidirect |
| 10. #23752179 | C2 | semidirect |
| 11. #520×C151 | C2 | semidirect |
| 21. #18012672 | C22 | semidirect |
| 22. #18012672 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012670 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. #18012670 | C22 | semidirect |
| 31. C22⋊(C151⋊C8) | C22 | semidirect |
| 32. C22⋊(C151⋊C8) | C22 | semidirect |
| 38. #117×C151 | C22 | semidirect |
| 40. C2×C4⋊C4×C151 | C22 | semidirect |
| 134. C151 | #3096 | semidirect |
| 137. #520 | D151 | semidirect |
| 161. #117 | C2×D151 | semidirect |
| 163. C2×C4⋊C4 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752776 | 2 |
| #23752536 | 2 |
| #23752530 | 2 |
| #23752525 | 2 |
| #23752252 | 2 |
| #23752248 | 2 |
| #23752216 | 2 |
| C2×#18012659 | 2 |
| #23752179 | 2 |
| #520×C151 | 2 |
| #3096 | 151 |