Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #23752556 | C2 | semidirect |
| 4. #23752555 | C2 | semidirect |
| 5. #23752549 | C2 | semidirect |
| 6. #23752544 | C2 | semidirect |
| 7. #23752255 | C2 | semidirect |
| 8. #23752220 | C2 | semidirect |
| 9. C2×#18012664 | C2 | semidirect |
| 11. #427×C151 | C2 | semidirect |
| 126. C151 | #3097 | semidirect |
| 135. #427 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752788 | 2 |
| #23752692 | 2 |
| #23752556 | 2 |
| #23752555 | 2 |
| #23752549 | 2 |
| #23752544 | 2 |
| #23752255 | 2 |
| #23752220 | 2 |
| C2×#18012664 | 2 |
| #23752178 | 2 |
| #427×C151 | 2 |
| #3097 | 151 |