Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #23752836 | C2 | semidirect |
| 2. #23752596 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752471 | C2 | semidirect |
| 6. #23752442 | C2 | semidirect |
| 7. #23752323 | C2 | semidirect |
| 8. #23752318 | C2 | semidirect |
| 9. #23752299 | C2 | semidirect |
| 10. #23752166 | C2 | semidirect |
| 11. #498×C151 | C2 | semidirect |
| 109. C151 | #3173 | semidirect |
| 112. #498 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752836 | 2 |
| #23752596 | 2 |
| #23752574 | 2 |
| #23752471 | 2 |
| #23752466 | 2 |
| #23752442 | 2 |
| #23752323 | 2 |
| #23752318 | 2 |
| #23752299 | 2 |
| #23752166 | 2 |
| #498×C151 | 2 |
| #3173 | 151 |