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. #23752471 | C2 | semidirect |
| 5. #23752470 | C2 | semidirect |
| 6. #23752467 | C2 | semidirect |
| 7. #23752452 | C2 | semidirect |
| 8. #23752451 | C2 | semidirect |
| 9. #23752247 | C2 | semidirect |
| 10. #23752219 | C2 | semidirect |
| 11. #470×C151 | C2 | semidirect |
| 133. C151 | #3059 | semidirect |
| 141. #470 | 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×#18012747 | 2 |
| #23752785 | 2 |
| #23752471 | 2 |
| #23752470 | 2 |
| #23752467 | 2 |
| #23752452 | 2 |
| #23752451 | 2 |
| #23752247 | 2 |
| #23752219 | 2 |
| #470×C151 | 2 |
| #3059 | 151 |