Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. C2×#18012786 | C2 | semidirect |
| 2. C2×#18012772 | C2 | semidirect |
| 3. C2×#18012759 | C2 | semidirect |
| 4. #23752793 | C2 | semidirect |
| 5. #23752375 | C2 | semidirect |
| 6. #23752369 | C2 | semidirect |
| 7. #23752358 | C2 | semidirect |
| 8. #23752352 | C2 | semidirect |
| 9. C2×#18012662 | C2 | semidirect |
| 10. #23752180 | C2 | semidirect |
| 11. #417×C151 | C2 | semidirect |
| 58. C2×Dic302 | D4 | semidirect |
| 87. #41×C151 | D4 | semidirect |
| 169. C151 | #3013 | semidirect |
| 179. #417 | D151 | semidirect |
| 224. #41 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012786 | 2 |
| C2×#18012772 | 2 |
| C2×#18012759 | 2 |
| #23752793 | 2 |
| #23752375 | 2 |
| #23752369 | 2 |
| #23752358 | 2 |
| #23752352 | 2 |
| C2×#18012662 | 2 |
| #23752180 | 2 |
| #417×C151 | 2 |
| #3013 | 151 |