Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#18012697 | C2 | semidirect |
| 3. #23752552 | C2 | semidirect |
| 4. #23752551 | C2 | semidirect |
| 5. #23752535 | C2 | semidirect |
| 6. #23752534 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. #23752252 | C2 | semidirect |
| 9. #23752213 | C2 | semidirect |
| 10. #23752175 | C2 | semidirect |
| 11. #417×C151 | C2 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. #18012671 | C22 | semidirect |
| 33. #18012670 | C22 | semidirect |
| 34. #18012663 | C22 | semidirect |
| 35. #18012660 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 42. #102×C151 | C22 | semidirect |
| 152. C151 | #3093 | semidirect |
| 163. #417 | D151 | semidirect |
| 191. #103 | C2×D151 | semidirect |
| 193. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752719 | 2 |
| C2×#18012697 | 2 |
| #23752552 | 2 |
| #23752551 | 2 |
| #23752535 | 2 |
| #23752534 | 2 |
| #23752254 | 2 |
| #23752252 | 2 |
| #23752213 | 2 |
| #23752175 | 2 |
| #417×C151 | 2 |
| #3093 | 151 |