Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012768 | C2 | semidirect |
| 2. C2×#18012763 | C2 | semidirect |
| 3. #23752760 | C2 | semidirect |
| 4. #124×D151 | C2 | semidirect |
| 5. #23752607 | C2 | semidirect |
| 6. #23752606 | C2 | semidirect |
| 7. #23752599 | C2 | semidirect |
| 8. #23752595 | C2 | semidirect |
| 9. #23752593 | C2 | semidirect |
| 10. #23752164 | C2 | semidirect |
| 11. #496×C151 | C2 | semidirect |
| 17. C2×Dic604 | C22 | semidirect |
| 18. C2×#14558994 | C22 | semidirect |
| 21. C2×#14558992 | C22 | semidirect |
| 24. #18012739 | C22 | semidirect |
| 28. #18012726 | C22 | semidirect |
| 34. #18012650 | C22 | semidirect |
| 35. C8×Dic151 | C22 | semidirect |
| 36. C2×SD16×C151 | C22 | semidirect |
| 38. #127×C151 | C22 | semidirect |
| 40. #97×C151 | C22 | semidirect |
| 62. #14558987 | D4 | semidirect |
| 134. C151 | #3153 | semidirect |
| 143. #496 | D151 | semidirect |
| 157. C2×SD16 | C2×D151 | semidirect |
| 162. #127 | C2×D151 | semidirect |
| 174. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012768 | 2 |
| C2×#18012763 | 2 |
| #23752760 | 2 |
| #124×D151 | 2 |
| #23752607 | 2 |
| #23752606 | 2 |
| #23752599 | 2 |
| #23752595 | 2 |
| #23752593 | 2 |
| #23752164 | 2 |
| #496×C151 | 2 |
| #3153 | 151 |