Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×D228 | C2 | semidirect |
| 2. C2×C3×D76 | C2 | semidirect |
| 3. C2×C19×C3⋊C8 | C2 | semidirect |
| 4. #11744819 | C2 | direct (N × H) |
| 10. D228 | C22 | semidirect |
| 12. C3×D76 | C22 | semidirect |
| 13. C19×C3⋊C8 | C22 | semidirect |
| 15. C2×D76 | D3 | semidirect |
| 31. D76 | C2×D3 | semidirect |
| 33. C2×C3×C19 | D8 | semidirect |
| 45. C3×C19 | C2×D8 | semidirect |
| 49. C2×C3⋊C8 | D19 | semidirect |
| 50. C2×C19 | #213 | semidirect |
| 62. C3⋊C8 | C2×D19 | semidirect |
| 63. C19 | C2×#213 | semidirect |
| 84. C2×C3 | D152 | semidirect |
| 94. C3 | C2×D152 | semidirect |
| 97. C2 | #11744819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D228 | 2 |
| C2×C3×D76 | 2 |
| C2×C19×C3⋊C8 | 2 |
| #11744819 | 2 |
| C2×D152 | 3 |
| C2×#213 | 19 |