Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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. C22×#14559005 | C2 | semidirect |
| 2. #23752763 | C2 | direct (N × H) |
| 3. C2×#18012736 | C2 | semidirect |
| 4. C2×#18012728 | C2 | semidirect |
| 5. C2×#18012714 | C2 | semidirect |
| 6. C2×#18012701 | C2 | semidirect |
| 7. C2×C42×D151 | C2 | semidirect |
| 8. C2×C4⋊Q8×C151 | C2 | semidirect |
| 10. C2×#14559005 | C22 | semidirect |
| 17. #18012736 | C22 | semidirect |
| 18. #18012728 | C22 | semidirect |
| 19. #18012714 | C22 | semidirect |
| 20. #18012701 | C22 | semidirect |
| 24. C42×D151 | C22 | semidirect |
| 26. C4⋊Q8×C151 | C22 | semidirect |
| 42. C2×C4×D151 | D4 | semidirect |
| 71. C4×D151 | C2×D4 | semidirect |
| 76. C2×C4×C151 | #41 | semidirect |
| 91. C4×C151 | C2×#41 | semidirect |
| 94. C2×C151 | #532 | semidirect |
| 99. C151 | C2×#532 | semidirect |
| 103. C2×C4⋊Q8 | D151 | semidirect |
| 118. C4⋊Q8 | C2×D151 | semidirect |
| 176. C2×C4 | #14559005 | semidirect |
| 193. C4 | C2×#14559005 | semidirect |
| 196. C2 | #23752763 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559005 | 2 |
| #23752763 | 2 |
| C2×#18012736 | 2 |
| C2×#18012728 | 2 |
| C2×#18012714 | 2 |
| C2×#18012701 | 2 |
| C2×C42×D151 | 2 |
| C2×C4⋊Q8×C151 | 2 |
| C2×#532 | 151 |