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. #23752556 | C2 | semidirect |
| 4. #23752555 | C2 | semidirect |
| 5. #23752539 | C2 | semidirect |
| 6. #23752538 | C2 | semidirect |
| 7. #23752255 | C2 | semidirect |
| 8. #23752214 | C2 | semidirect |
| 9. #23752211 | C2 | semidirect |
| 10. #23752175 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 30. #18012672 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. #18012664 | C22 | semidirect |
| 33. #18012662 | C22 | semidirect |
| 34. #18012661 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 41. #107×C151 | C22 | semidirect |
| 42. #106×C151 | C22 | semidirect |
| 152. C151 | #3093 | semidirect |
| 161. #428 | D151 | semidirect |
| 187. #107 | C2×D151 | semidirect |
| 189. #106 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752724 | 2 |
| C2×#18012697 | 2 |
| #23752556 | 2 |
| #23752555 | 2 |
| #23752539 | 2 |
| #23752538 | 2 |
| #23752255 | 2 |
| #23752214 | 2 |
| #23752211 | 2 |
| #23752175 | 2 |
| #428×C151 | 2 |
| #3093 | 151 |