Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D151 | C2 | semidirect |
| 3. C2×#18012715 | C2 | semidirect |
| 4. #23752467 | C2 | semidirect |
| 5. #23752455 | C2 | semidirect |
| 6. #23752450 | C2 | semidirect |
| 7. #23752438 | C2 | semidirect |
| 8. #23752254 | C2 | semidirect |
| 9. #23752221 | C2 | semidirect |
| 10. #23752213 | C2 | semidirect |
| 11. C2×#137×C151 | C2 | semidirect |
| 33. #18012673 | C22 | semidirect |
| 34. #18012671 | C22 | semidirect |
| 35. #18012663 | C22 | semidirect |
| 36. #18012663 | C22 | semidirect |
| 37. #18012663 | C22 | semidirect |
| 38. #18012660 | C22 | semidirect |
| 42. C2×Q16×C151 | C22 | semidirect |
| 43. C2×SD16×C151 | C22 | semidirect |
| 90. M16×C151 | D4 | semidirect |
| 145. C2×D151 | #137 | semidirect |
| 163. C151 | #3056 | semidirect |
| 165. C2×#137 | D151 | semidirect |
| 180. C2×Q16 | C2×D151 | semidirect |
| 181. C2×SD16 | C2×D151 | semidirect |
| 236. M16 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D151 | 2 |
| #23752719 | 2 |
| C2×#18012715 | 2 |
| #23752467 | 2 |
| #23752455 | 2 |
| #23752450 | 2 |
| #23752438 | 2 |
| #23752254 | 2 |
| #23752221 | 2 |
| #23752213 | 2 |
| C2×#137×C151 | 2 |
| #3056 | 151 |