Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D151 | C2 | semidirect |
| 4. #23752469 | C2 | semidirect |
| 5. #23752468 | C2 | semidirect |
| 6. #23752454 | C2 | semidirect |
| 7. #23752453 | C2 | semidirect |
| 8. #23752450 | C2 | semidirect |
| 9. #23752249 | C2 | semidirect |
| 10. #23752219 | C2 | semidirect |
| 11. #467×C151 | C2 | semidirect |
| 137. C151 | #3059 | semidirect |
| 147. #467 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D151 | 2 |
| C2×#18012745 | 2 |
| #23752785 | 2 |
| #23752469 | 2 |
| #23752468 | 2 |
| #23752454 | 2 |
| #23752453 | 2 |
| #23752450 | 2 |
| #23752249 | 2 |
| #23752219 | 2 |
| #467×C151 | 2 |
| #3059 | 151 |