Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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. #11744989 | C2 | semidirect |
| 2. #11744938 | C2 | semidirect |
| 3. C19×#215 | C2 | semidirect |
| 4. C3×#64527 | C2 | semidirect |
| 5. #11744820 | C2 | semidirect |
| 6. #11744819 | C2 | semidirect |
| 7. #11744817 | C2 | semidirect |
| 10. C3×Q8×C19 | C22 | semidirect |
| 12. D228 | 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 |
| 60. C3×C19 | AGL(1,ℤ/8) | semidirect |
| 64. #215 | D19 | semidirect |
| 75. C3×Q8 | C2×D19 | semidirect |
| 84. C3⋊C8 | C2×D19 | semidirect |
| 85. C19 | #914 | semidirect |
| 102. Q8 | D3×D19 | semidirect |
| 125. C3 | #10597360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744989 | 2 |
| #11744938 | 2 |
| C19×#215 | 2 |
| C3×#64527 | 2 |
| #11744820 | 2 |
| #11744819 | 2 |
| #11744817 | 2 |
| #10597360 | 3 |
| #914 | 19 |