Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #23752578 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752569 | C2 | semidirect |
| 5. #23752560 | C2 | semidirect |
| 6. #23752216 | C2 | semidirect |
| 7. #23752211 | C2 | semidirect |
| 8. #23752206 | C2 | semidirect |
| 9. C2×#18012659 | C2 | semidirect |
| 10. #23752168 | C2 | semidirect |
| 11. #544×C151 | C2 | semidirect |
| 21. #18012662 | C22 | semidirect |
| 22. #18012662 | C22 | semidirect |
| 23. #18012662 | C22 | semidirect |
| 28. #18012659 | C22 | semidirect |
| 29. #18012659 | C22 | semidirect |
| 30. #18012659 | C22 | semidirect |
| 31. #18012650 | C22 | semidirect |
| 32. C4×C151⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C151 | C22 | semidirect |
| 36. #125×C151 | C22 | semidirect |
| 135. C151 | #3136 | semidirect |
| 137. #544 | D151 | semidirect |
| 153. C4⋊Q8 | C2×D151 | semidirect |
| 156. #125 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752781 | 2 |
| #23752578 | 2 |
| #23752574 | 2 |
| #23752569 | 2 |
| #23752560 | 2 |
| #23752216 | 2 |
| #23752211 | 2 |
| #23752206 | 2 |
| C2×#18012659 | 2 |
| #23752168 | 2 |
| #544×C151 | 2 |
| #3136 | 151 |