Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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. Q8×D57 | C2 | semidirect |
| 3. C19×#215 | C2 | semidirect |
| 4. C3×#64527 | C2 | semidirect |
| 5. #11744825 | C2 | semidirect |
| 6. #11744823 | C2 | semidirect |
| 7. D57⋊C8 | C2 | semidirect |
| 10. C3×Q8×C19 | C22 | semidirect |
| 14. Dic114 | C22 | semidirect |
| 18. C3×C19⋊C8 | C22 | semidirect |
| 19. C19×C3⋊C8 | C22 | semidirect |
| 23. #64527 | D3 | semidirect |
| 36. Q8×C19 | C2×D3 | semidirect |
| 45. C19⋊C8 | C2×D3 | semidirect |
| 47. D57 | SD16 | semidirect |
| 59. C3×C19 | C2×SD16 | semidirect |
| 63. #215 | D19 | semidirect |
| 73. C3×Q8 | C2×D19 | semidirect |
| 82. C3⋊C8 | C2×D19 | semidirect |
| 83. C19 | D3×SD16 | semidirect |
| 102. Q8 | D3×D19 | semidirect |
| 122. C3 | SD16×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D57 | 2 |
| #11744938 | 2 |
| C19×#215 | 2 |
| C3×#64527 | 2 |
| #11744825 | 2 |
| #11744823 | 2 |
| D57⋊C8 | 2 |
| SD16×D19 | 3 |
| D3×SD16 | 19 |