Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23752919 | C2 | semidirect |
| 3. #23752559 | C2 | semidirect |
| 4. #23752531 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752441 | C2 | semidirect |
| 7. #23752413 | C2 | semidirect |
| 8. #23752365 | C2 | semidirect |
| 9. C4×#14558993 | C2 | semidirect |
| 10. C2×#18012661 | C2 | semidirect |
| 11. C8×D4×C151 | C2 | semidirect |
| 15. C2×#14558993 | C22 | semidirect |
| 16. #18012739 | C22 | semidirect |
| 19. #18012718 | C22 | semidirect |
| 24. C4×Dic302 | C22 | semidirect |
| 27. C2×C4⋊Dic151 | C22 | semidirect |
| 28. #18012671 | C22 | semidirect |
| 29. #18012671 | C22 | semidirect |
| 30. #18012664 | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012661 | C22 | semidirect |
| 35. #18012661 | C22 | semidirect |
| 36. C22×C8×C151 | C22 | semidirect |
| 38. C4⋊C8×C151 | C22 | semidirect |
| 39. C22⋊C8×C151 | C22 | semidirect |
| 40. C4×C8×C151 | C22 | semidirect |
| 100. D4×C151 | SD16 | semidirect |
| 136. C151 | #3295 | semidirect |
| 147. C8×D4 | D151 | semidirect |
| 153. C22×C8 | C2×D151 | semidirect |
| 169. C4⋊C8 | C2×D151 | semidirect |
| 176. C22⋊C8 | C2×D151 | semidirect |
| 177. C4×C8 | C2×D151 | semidirect |
| 231. D4 | #14558993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752919 | 2 |
| D4×D604 | 2 |
| #23752559 | 2 |
| #23752531 | 2 |
| #23752503 | 2 |
| #23752441 | 2 |
| #23752413 | 2 |
| #23752365 | 2 |
| C4×#14558993 | 2 |
| C2×#18012661 | 2 |
| C8×D4×C151 | 2 |
| #3295 | 151 |