Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 44 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. #11744985 | C2 | semidirect |
| 2. C19×#235 | C2 | semidirect |
| 3. C2×C3×C19⋊C8 | C2 | semidirect |
| 4. #11744829 | C2 | semidirect |
| 5. #11744826 | C2 | semidirect |
| 6. #11744825 | C2 | semidirect |
| 7. #11744820 | C2 | semidirect |
| 26. C2×C19⋊C8 | D3 | semidirect |
| 57. C3×C19 | #135 | semidirect |
| 59. #235 | D19 | semidirect |
| 81. C19 | #904 | semidirect |
| 118. C3 | #10597396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744985 | 2 |
| C19×#235 | 2 |
| C2×C3×C19⋊C8 | 2 |
| #11744829 | 2 |
| #11744826 | 2 |
| #11744825 | 2 |
| #11744820 | 2 |
| #10597396 | 3 |
| #904 | 19 |