Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752762 | C2 | semidirect |
| 2. C2×#18012727 | C2 | semidirect |
| 3. #23752601 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752428 | C2 | semidirect |
| 6. #23752353 | C2 | semidirect |
| 7. #23752348 | C2 | semidirect |
| 8. #432×C151 | C2 | semidirect |
| 12. C2×#14558993 | C22 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 15. #18012736 | C22 | semidirect |
| 24. C4×D604 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 30. C4⋊C8×C151 | C22 | semidirect |
| 32. #97×C151 | C22 | semidirect |
| 120. C151 | #3213 | semidirect |
| 129. #432 | D151 | semidirect |
| 149. C4⋊C8 | C2×D151 | semidirect |
| 153. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| C2×#18012727 | 2 |
| #23752601 | 2 |
| #23752572 | 2 |
| #23752428 | 2 |
| #23752353 | 2 |
| #23752348 | 2 |
| #432×C151 | 2 |
| #3213 | 151 |