Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #23752843 | C2 | semidirect |
| 3. #23752579 | C2 | semidirect |
| 4. #23752570 | C2 | semidirect |
| 5. #23752565 | C2 | semidirect |
| 6. #23752561 | C2 | semidirect |
| 7. #23752222 | C2 | semidirect |
| 9. C2×#18012662 | C2 | semidirect |
| 10. #23752170 | C2 | semidirect |
| 127. C151 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752843 | 2 |
| #23752783 | 2 |
| #23752579 | 2 |
| #23752570 | 2 |
| #23752565 | 2 |
| #23752561 | 2 |
| #23752222 | 2 |
| #23752208 | 2 |
| C2×#18012662 | 2 |
| #23752170 | 2 |
| #417×C151 | 2 |
| #3137 | 151 |