Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752922 | C2 | semidirect |
| 3. #23752559 | C2 | semidirect |
| 4. #23752532 | C2 | semidirect |
| 5. #23752502 | C2 | semidirect |
| 6. #23752444 | C2 | semidirect |
| 7. #23752412 | C2 | semidirect |
| 8. #23752361 | C2 | semidirect |
| 9. C8×D604 | C2 | semidirect |
| 10. #102×D151 | C2 | semidirect |
| 11. C4×SD16×C151 | C2 | semidirect |
| 14. C2×#14558991 | C22 | semidirect |
| 15. C2×C8×D151 | C22 | semidirect |
| 16. #18012739 | C22 | semidirect |
| 20. #18012715 | C22 | semidirect |
| 26. C4⋊C4×D151 | C22 | semidirect |
| 27. #18012670 | C22 | semidirect |
| 28. C4⋊(C151⋊C8) | C22 | semidirect |
| 29. #18012661 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 32. #18012659 | C22 | semidirect |
| 33. (C2×D151)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C151 | C22 | semidirect |
| 37. #106×C151 | C22 | semidirect |
| 38. #103×C151 | C22 | semidirect |
| 40. C4×C8×C151 | C22 | semidirect |
| 88. D604 | SD16 | semidirect |
| 136. C151 | #3295 | semidirect |
| 146. C4×SD16 | D151 | semidirect |
| 162. C4×Q8 | C2×D151 | semidirect |
| 168. #106 | C2×D151 | semidirect |
| 170. #103 | C2×D151 | semidirect |
| 177. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752922 | 2 |
| D4×D604 | 2 |
| #23752559 | 2 |
| #23752532 | 2 |
| #23752502 | 2 |
| #23752444 | 2 |
| #23752412 | 2 |
| #23752361 | 2 |
| C8×D604 | 2 |
| #102×D151 | 2 |
| C4×SD16×C151 | 2 |
| #3295 | 151 |