Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 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. C19×#237 | C2 | semidirect |
| 2. #11744930 | C2 | semidirect |
| 3. #11744890 | C2 | semidirect |
| 4. C3×#64526 | C2 | semidirect |
| 5. #11744827 | C2 | semidirect |
| 6. #11744826 | C2 | semidirect |
| 7. D3×C19⋊C8 | C2 | semidirect |
| 24. #64526 | D3 | semidirect |
| 57. C3×C19 | #135 | semidirect |
| 59. #237 | D19 | semidirect |
| 81. C19 | #916 | semidirect |
| 118. C3 | #10597396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#237 | 2 |
| #11744930 | 2 |
| #11744890 | 2 |
| C3×#64526 | 2 |
| #11744827 | 2 |
| #11744826 | 2 |
| D3×C19⋊C8 | 2 |
| #10597396 | 3 |
| #916 | 19 |