Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #23752695 | C2 | semidirect |
| 3. #23752218 | C2 | semidirect |
| 4. #23752214 | C2 | semidirect |
| 5. #23752209 | C2 | semidirect |
| 6. C2×#18012661 | C2 | semidirect |
| 7. C2×#131×C151 | C2 | semidirect |
| 9. #18012785 | C4 | semidirect |
| 16. #18012698 | C22 | semidirect |
| 17. C2×C4⋊Dic151 | C22 | semidirect |
| 18. #18012664 | C22 | semidirect |
| 19. #18012664 | C22 | semidirect |
| 20. #18012661 | C22 | semidirect |
| 21. #18012661 | C22 | semidirect |
| 22. #18012661 | C22 | semidirect |
| 25. C2×M16×C151 | C22 | semidirect |
| 26. C22×C8×C151 | C22 | semidirect |
| 30. #14559004 | C2×C4 | semidirect |
| 34. C2×D604 | C2×C4 | semidirect |
| 97. C151 | #2897 | semidirect |
| 100. C2×#131 | D151 | semidirect |
| 114. C2×M16 | C2×D151 | semidirect |
| 115. C22×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012785 | 2 |
| #23752695 | 2 |
| #23752218 | 2 |
| #23752214 | 2 |
| #23752209 | 2 |
| C2×#18012661 | 2 |
| C2×#131×C151 | 2 |
| #2897 | 151 |