Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14559003 | C2 | semidirect |
| 2. C2×#18012758 | C2 | semidirect |
| 3. #23752722 | C2 | semidirect |
| 4. #23752375 | C2 | semidirect |
| 5. #23752370 | C2 | semidirect |
| 6. #23752363 | C2 | semidirect |
| 7. #23752354 | C2 | semidirect |
| 8. #23752350 | C2 | semidirect |
| 9. #23752205 | C2 | semidirect |
| 10. C22⋊C8×D151 | C2 | semidirect |
| 11. #447×C151 | C2 | semidirect |
| 17. C2×#14559003 | C22 | semidirect |
| 23. C2×Dic604 | C22 | semidirect |
| 24. C2×#14558992 | C22 | semidirect |
| 25. C2×#14558992 | C22 | semidirect |
| 26. C2×C8×D151 | C22 | semidirect |
| 28. #18012719 | C22 | semidirect |
| 30. #18012710 | C22 | semidirect |
| 34. #18012697 | C22 | semidirect |
| 35. #18012664 | C22 | semidirect |
| 36. #18012662 | C22 | semidirect |
| 37. #18012660 | C22 | semidirect |
| 39. (C2×D151)⋊C8 | C22 | semidirect |
| 41. C2×D8×C151 | C22 | semidirect |
| 43. #102×C151 | C22 | semidirect |
| 52. #14559003 | D4 | semidirect |
| 150. C22×C151 | #135 | semidirect |
| 175. C151 | #3002 | semidirect |
| 185. #447 | D151 | semidirect |
| 203. C2×D8 | C2×D151 | semidirect |
| 217. #102 | C2×D151 | semidirect |
| 333. C22 | #18012758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559003 | 2 |
| C2×#18012758 | 2 |
| #23752722 | 2 |
| #23752375 | 2 |
| #23752370 | 2 |
| #23752363 | 2 |
| #23752354 | 2 |
| #23752350 | 2 |
| #23752205 | 2 |
| C22⋊C8×D151 | 2 |
| #447×C151 | 2 |
| #3002 | 151 |