Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 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. C22×Q8×D151 | C2 | semidirect |
| 2. C2×#18012768 | C2 | semidirect |
| 4. #23752370 | C2 | semidirect |
| 5. #23752369 | C2 | semidirect |
| 6. #23752368 | C2 | semidirect |
| 7. #23752350 | C2 | semidirect |
| 8. #23752349 | C2 | semidirect |
| 9. #23752219 | C2 | semidirect |
| 10. #23752174 | C2 | semidirect |
| 11. #448×C151 | C2 | semidirect |
| 23. C2×Dic604 | C22 | semidirect |
| 24. C2×#14558994 | C22 | semidirect |
| 25. C2×#14558992 | C22 | semidirect |
| 35. #18012664 | C22 | semidirect |
| 36. #18012663 | C22 | semidirect |
| 37. #18012662 | C22 | semidirect |
| 41. C2×SD16×C151 | C22 | semidirect |
| 43. #103×C151 | C22 | semidirect |
| 59. Q8×D151 | D4 | semidirect |
| 144. C22×C151 | #137 | semidirect |
| 152. C2×D151 | #137 | semidirect |
| 169. C151 | #3004 | semidirect |
| 179. #448 | D151 | semidirect |
| 197. C2×SD16 | C2×D151 | semidirect |
| 211. #103 | C2×D151 | semidirect |
| 321. C22 | #18012768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D151 | 2 |
| C2×#18012768 | 2 |
| #23752722 | 2 |
| #23752370 | 2 |
| #23752369 | 2 |
| #23752368 | 2 |
| #23752350 | 2 |
| #23752349 | 2 |
| #23752219 | 2 |
| #23752174 | 2 |
| #448×C151 | 2 |
| #3004 | 151 |