Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23752940 | C2 | semidirect |
| 3. #23752567 | C2 | semidirect |
| 5. #23752513 | C2 | semidirect |
| 6. #23752498 | C2 | semidirect |
| 7. #23752435 | C2 | semidirect |
| 9. C4×Dic604 | C2 | semidirect |
| 10. C4×#14558993 | C2 | semidirect |
| 11. C8×Q8×C151 | C2 | semidirect |
| 117. C151 | #3365 | semidirect |
| 127. C8×Q8 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752947 | 2 |
| #23752940 | 2 |
| #23752567 | 2 |
| #23752559 | 2 |
| #23752513 | 2 |
| #23752498 | 2 |
| #23752435 | 2 |
| #23752413 | 2 |
| C4×Dic604 | 2 |
| C4×#14558993 | 2 |
| C8×Q8×C151 | 2 |
| #3365 | 151 |