Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #23752746 | C2 | semidirect |
| 2. #23752512 | C2 | semidirect |
| 3. #23752504 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752446 | C2 | semidirect |
| 6. #23752439 | C2 | semidirect |
| 7. #23752427 | C2 | semidirect |
| 8. #23752409 | C2 | semidirect |
| 9. #23752404 | C2 | semidirect |
| 10. C2×C4⋊(C151⋊C8) | C2 | semidirect |
| 11. #532×C151 | C2 | semidirect |
| 141. C151 | #3247 | semidirect |
| 143. #532 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752512 | 2 |
| #23752504 | 2 |
| #23752499 | 2 |
| #23752446 | 2 |
| #23752439 | 2 |
| #23752427 | 2 |
| #23752409 | 2 |
| #23752404 | 2 |
| C2×C4⋊(C151⋊C8) | 2 |
| #532×C151 | 2 |
| #3247 | 151 |