Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #23752867 | C2 | semidirect |
| 2. #23752564 | C2 | semidirect |
| 3. #23752553 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752439 | C2 | semidirect |
| 6. #23752417 | C2 | semidirect |
| 7. #23752355 | C2 | semidirect |
| 8. C4×#14558989 | C2 | semidirect |
| 9. D4×C151⋊C8 | C2 | semidirect |
| 10. #23752206 | C2 | semidirect |
| 11. #555×C151 | C2 | semidirect |
| 130. C151 | #3303 | semidirect |
| 132. #555 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752867 | 2 |
| #23752564 | 2 |
| #23752553 | 2 |
| #23752499 | 2 |
| #23752439 | 2 |
| #23752417 | 2 |
| #23752355 | 2 |
| C4×#14558989 | 2 |
| D4×C151⋊C8 | 2 |
| #23752206 | 2 |
| #555×C151 | 2 |
| #3303 | 151 |