Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #23752928 | C2 | direct (N × H) |
| 2. C2×#18012728 | C2 | semidirect |
| 3. C2×#18012714 | C2 | semidirect |
| 4. C2×C4×D604 | C2 | semidirect |
| 5. C2×#18012697 | C2 | semidirect |
| 6. C2×C4⋊Q8×C151 | C2 | semidirect |
| 10. #18012728 | C22 | semidirect |
| 11. #18012714 | C22 | semidirect |
| 12. C4×D604 | C22 | semidirect |
| 13. #18012697 | C22 | semidirect |
| 19. C4⋊Q8×C151 | C22 | semidirect |
| 69. C2×C151 | #555 | semidirect |
| 73. C151 | C2×#555 | semidirect |
| 76. C2×C4⋊Q8 | D151 | semidirect |
| 85. C4⋊Q8 | C2×D151 | semidirect |
| 144. C2 | #23752928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752928 | 2 |
| C2×#18012728 | 2 |
| C2×#18012714 | 2 |
| C2×C4×D604 | 2 |
| C2×#18012697 | 2 |
| C2×C4⋊Q8×C151 | 2 |
| C2×#555 | 151 |