Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012770 | C2 | semidirect |
| 3. #23752786 | C2 | semidirect |
| 4. #23752373 | C2 | semidirect |
| 5. #23752366 | C2 | semidirect |
| 6. #23752221 | C2 | semidirect |
| 7. #23752209 | C2 | semidirect |
| 8. #23752178 | C2 | semidirect |
| 9. C22×Q16×C151 | C2 | semidirect |
| 140. C151 | #3011 | semidirect |
| 144. C22×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012787 | 2 |
| C2×#18012770 | 2 |
| #23752786 | 2 |
| #23752373 | 2 |
| #23752366 | 2 |
| #23752221 | 2 |
| #23752209 | 2 |
| #23752178 | 2 |
| C22×Q16×C151 | 2 |
| #3011 | 151 |