Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 2. #11744885 | C2 | semidirect |
| 3. C19×#208 | C2 | semidirect |
| 4. #11744815 | C2 | semidirect |
| 5. C3⋊C8×D19 | C2 | semidirect |
| 14. C3⋊(C19⋊C8) | C22 | semidirect |
| 15. C19×C3⋊C8 | C22 | semidirect |
| 41. C3×D19 | M16 | semidirect |
| 51. C3×C19 | C2×M16 | semidirect |
| 55. #208 | D19 | direct (N × H) |
| 60. D19 | #208 | direct (N × H) |
| 70. C3⋊C8 | C2×D19 | semidirect |
| 71. C19 | C2×#208 | semidirect |
| 106. C3 | M16×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D19 | 2 |
| #11744885 | 2 |
| C19×#208 | 2 |
| #11744815 | 2 |
| C3⋊C8×D19 | 2 |
| M16×D19 | 3 |
| C2×#208 | 19 |