Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23752978 | C2 | semidirect |
| 3. #23752230 | C2 | semidirect |
| 4. C2×#18012656 | C2 | semidirect |
| 5. #23751982 | C2 | semidirect |
| 6. C151⋊#338 | C2 | semidirect |
| 7. #418×C151 | C2 | semidirect |
| 11. C2×#14558992 | C4 | semidirect |
| 12. C2×#14558989 | C4 | semidirect |
| 112. C151 | #1903 | semidirect |
| 117. #418 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| #23752978 | 2 |
| #23752230 | 2 |
| C2×#18012656 | 2 |
| #23751982 | 2 |
| C151⋊#338 | 2 |
| #418×C151 | 2 |
| #1903 | 151 |