Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752582 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752569 | C2 | semidirect |
| 5. #23752564 | C2 | semidirect |
| 6. #23752220 | C2 | semidirect |
| 9. C2×#18012662 | C2 | semidirect |
| 10. #23752168 | C2 | semidirect |
| 11. #544×C151 | C2 | semidirect |
| 127. C151 | #3137 | semidirect |
| 129. #544 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752788 | 2 |
| #23752582 | 2 |
| #23752574 | 2 |
| #23752569 | 2 |
| #23752564 | 2 |
| #23752220 | 2 |
| #23752211 | 2 |
| #23752206 | 2 |
| C2×#18012662 | 2 |
| #23752168 | 2 |
| #544×C151 | 2 |
| #3137 | 151 |