Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752769 | C2 | semidirect |
| 3. #23752621 | C2 | semidirect |
| 4. #23752606 | C2 | semidirect |
| 5. #23752581 | C2 | semidirect |
| 6. #23752572 | C2 | semidirect |
| 7. #23752470 | C2 | semidirect |
| 9. C4×Dic604 | C2 | semidirect |
| 10. C4×#14558993 | C2 | semidirect |
| 11. C4×M16×C151 | C2 | semidirect |
| 129. C151 | #3172 | semidirect |
| 141. C4×M16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752746 | 2 |
| #23752621 | 2 |
| #23752606 | 2 |
| #23752581 | 2 |
| #23752572 | 2 |
| #23752470 | 2 |
| #23752458 | 2 |
| C4×Dic604 | 2 |
| C4×#14558993 | 2 |
| C4×M16×C151 | 2 |
| #3172 | 151 |