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. #23752573 | C2 | semidirect |
| 5. #23752568 | C2 | semidirect |
| 6. #23752561 | C2 | semidirect |
| 7. #23752221 | C2 | semidirect |
| 10. #23752167 | C2 | semidirect |
| 11. C2×#103×C151 | C2 | semidirect |
| 127. C151 | #3137 | semidirect |
| 138. C2×#103 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752843 | 2 |
| #23752786 | 2 |
| #23752579 | 2 |
| #23752573 | 2 |
| #23752568 | 2 |
| #23752561 | 2 |
| #23752221 | 2 |
| #23752211 | 2 |
| #23752209 | 2 |
| #23752167 | 2 |
| C2×#103×C151 | 2 |
| #3137 | 151 |