Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23752767 | C2 | semidirect |
| 3. #23752521 | C2 | semidirect |
| 4. #23752515 | C2 | semidirect |
| 5. #23752499 | C2 | semidirect |
| 6. #23752497 | C2 | semidirect |
| 7. #23752493 | C2 | semidirect |
| 8. #23752249 | C2 | semidirect |
| 9. C4⋊C8×D151 | C2 | semidirect |
| 11. #477×C151 | C2 | semidirect |
| 44. #14559005 | Q8 | semidirect |
| 134. C151 | #3076 | semidirect |
| 140. #477 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| C4×#14559005 | 2 |
| #23752521 | 2 |
| #23752515 | 2 |
| #23752499 | 2 |
| #23752497 | 2 |
| #23752493 | 2 |
| #23752249 | 2 |
| C4⋊C8×D151 | 2 |
| #23752207 | 2 |
| #477×C151 | 2 |
| #3076 | 151 |