Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012787 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752356 | C2 | semidirect |
| 5. #23752349 | C2 | semidirect |
| 6. #23752221 | C2 | semidirect |
| 7. #23752209 | C2 | semidirect |
| 8. #23752178 | C2 | semidirect |
| 9. C22×SD16×C151 | C2 | semidirect |
| 13. C2×#14559005 | C22 | semidirect |
| 18. C2×Q8×D151 | C22 | semidirect |
| 28. #18012664 | C22 | semidirect |
| 29. #18012663 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 31. (C2×D151)⋊C8 | C22 | semidirect |
| 44. #14559004 | D4 | semidirect |
| 72. C2×Q8×C151 | D4 | semidirect |
| 145. C151 | #3010 | semidirect |
| 149. C22×SD16 | D151 | semidirect |
| 200. C2×Q8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012787 | 2 |
| C2×#18012765 | 2 |
| #23752779 | 2 |
| #23752356 | 2 |
| #23752349 | 2 |
| #23752221 | 2 |
| #23752209 | 2 |
| #23752178 | 2 |
| C22×SD16×C151 | 2 |
| #3010 | 151 |