Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #23752767 | C2 | semidirect |
| 3. #23752575 | C2 | semidirect |
| 4. #23752560 | C2 | semidirect |
| 5. #23752559 | C2 | semidirect |
| 6. #23752558 | C2 | semidirect |
| 7. #23752215 | C2 | semidirect |
| 8. C4×#14558987 | C2 | semidirect |
| 9. #486×C151 | C2 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 19. #18012730 | C22 | semidirect |
| 26. #18012661 | C22 | semidirect |
| 27. #18012660 | C22 | semidirect |
| 28. #18012659 | C22 | semidirect |
| 29. #18012649 | C22 | semidirect |
| 30. C4×C151⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C151 | C22 | semidirect |
| 33. #102×C151 | C22 | semidirect |
| 34. C4×C8×C151 | C22 | semidirect |
| 123. C151 | #3138 | semidirect |
| 131. #486 | D151 | semidirect |
| 139. C4⋊Q8 | C2×D151 | semidirect |
| 155. #102 | C2×D151 | semidirect |
| 158. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #127×D151 | 2 |
| #23752575 | 2 |
| #23752560 | 2 |
| #23752559 | 2 |
| #23752558 | 2 |
| #23752215 | 2 |
| C4×#14558987 | 2 |
| #486×C151 | 2 |
| #3138 | 151 |