Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #23752569 | C2 | semidirect |
| 4. #23752509 | C2 | semidirect |
| 5. #23752494 | C2 | semidirect |
| 6. #23752434 | C2 | semidirect |
| 8. Q8×C151⋊C8 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 10. C4×#14558991 | C2 | semidirect |
| 11. #557×C151 | C2 | semidirect |
| 117. C151 | #3365 | semidirect |
| 120. #557 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752947 | 2 |
| #23752569 | 2 |
| #23752560 | 2 |
| #23752509 | 2 |
| #23752494 | 2 |
| #23752434 | 2 |
| #23752412 | 2 |
| Q8×C151⋊C8 | 2 |
| C4×#14558994 | 2 |
| C4×#14558991 | 2 |
| #557×C151 | 2 |
| #3365 | 151 |