Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#18012767 | C2 | semidirect |
| 2. C22×D1208 | C2 | semidirect |
| 3. #23752781 | C2 | semidirect |
| 4. #23752686 | C2 | semidirect |
| 5. #23752428 | C2 | semidirect |
| 6. #23752408 | C2 | semidirect |
| 7. #23752218 | C2 | semidirect |
| 8. #23752209 | C2 | semidirect |
| 9. #424×C151 | C2 | semidirect |
| 14. C2×#14558993 | C22 | semidirect |
| 17. C2×D1208 | C22 | semidirect |
| 18. #18012736 | C22 | semidirect |
| 19. #18012727 | C22 | semidirect |
| 22. C4×D604 | C22 | semidirect |
| 26. #18012664 | C22 | semidirect |
| 27. #18012661 | C22 | semidirect |
| 28. #18012661 | C22 | semidirect |
| 32. C4⋊C8×C151 | C22 | semidirect |
| 44. C2×D604 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 129. #424 | D151 | semidirect |
| 151. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C22×D1208 | 2 |
| #23752781 | 2 |
| #23752686 | 2 |
| #23752428 | 2 |
| #23752408 | 2 |
| #23752218 | 2 |
| #23752209 | 2 |
| #424×C151 | 2 |
| #3041 | 151 |