Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752783 | C2 | semidirect |
| 3. #23752554 | C2 | semidirect |
| 4. #23752537 | C2 | semidirect |
| 5. #23752458 | C2 | semidirect |
| 6. #23752441 | C2 | semidirect |
| 7. #23752365 | C2 | semidirect |
| 8. #23752353 | C2 | semidirect |
| 9. #408×C151 | C2 | semidirect |
| 10. C22×Dic302 | C22 | semidirect |
| 21. #18012718 | C22 | semidirect |
| 27. #18012698 | C22 | semidirect |
| 28. #18012673 | C22 | semidirect |
| 29. #18012671 | C22 | semidirect |
| 30. #18012664 | C22 | semidirect |
| 31. #18012664 | C22 | semidirect |
| 35. C2×M16×C151 | C22 | semidirect |
| 36. C22×C8×C151 | C22 | semidirect |
| 38. C22⋊C8×C151 | C22 | semidirect |
| 137. C151 | #3200 | semidirect |
| 147. #408 | D151 | semidirect |
| 153. C2×M16 | C2×D151 | semidirect |
| 154. C22×C8 | C2×D151 | semidirect |
| 176. C22⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752783 | 2 |
| #23752776 | 2 |
| #23752554 | 2 |
| #23752537 | 2 |
| #23752458 | 2 |
| #23752441 | 2 |
| #23752365 | 2 |
| #23752353 | 2 |
| #408×C151 | 2 |
| #3200 | 151 |