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×#18012767 | C2 | semidirect |
| 3. C22×#14558991 | C2 | semidirect |
| 4. #23752781 | C2 | semidirect |
| 5. #23752360 | C2 | semidirect |
| 6. #23752352 | C2 | semidirect |
| 7. #23752206 | C2 | semidirect |
| 8. #23752180 | C2 | semidirect |
| 9. #419×C151 | C2 | semidirect |
| 13. C2×#14559005 | C22 | semidirect |
| 18. C2×Q8×D151 | C22 | semidirect |
| 30. #18012662 | C22 | semidirect |
| 31. #18012659 | C22 | semidirect |
| 32. (C2×D151)⋊C8 | C22 | semidirect |
| 36. #103×C151 | C22 | semidirect |
| 45. #14559004 | D4 | semidirect |
| 74. C2×Q8×C151 | D4 | semidirect |
| 145. C151 | #3010 | semidirect |
| 153. #419 | D151 | semidirect |
| 180. #103 | C2×D151 | semidirect |
| 200. C2×Q8 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012787 | 2 |
| C2×#18012767 | 2 |
| C22×#14558991 | 2 |
| #23752781 | 2 |
| #23752360 | 2 |
| #23752352 | 2 |
| #23752206 | 2 |
| #23752180 | 2 |
| #419×C151 | 2 |
| #3010 | 151 |