Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#18012698 | C2 | semidirect |
| 3. #23752554 | C2 | semidirect |
| 4. #23752548 | C2 | semidirect |
| 5. #23752543 | C2 | semidirect |
| 6. #23752537 | C2 | semidirect |
| 7. #23752531 | C2 | semidirect |
| 8. #23752526 | C2 | semidirect |
| 9. #23752250 | C2 | semidirect |
| 10. #23752209 | C2 | semidirect |
| 11. C2×C22⋊C8×C151 | C2 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012673 | C22 | semidirect |
| 32. #18012671 | C22 | semidirect |
| 33. #18012671 | C22 | semidirect |
| 34. #18012664 | C22 | semidirect |
| 35. #18012664 | C22 | semidirect |
| 36. #18012661 | C22 | semidirect |
| 37. #18012661 | C22 | semidirect |
| 143. C151 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752723 | 2 |
| C2×#18012698 | 2 |
| #23752554 | 2 |
| #23752548 | 2 |
| #23752543 | 2 |
| #23752537 | 2 |
| #23752531 | 2 |
| #23752526 | 2 |
| #23752250 | 2 |
| #23752209 | 2 |
| C2×C22⋊C8×C151 | 2 |
| #3091 | 151 |