Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
188 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D19 |
| commutator, socle, cosocle | C22×C3×C19 | C23 |
| Fitting | C2×C3×C4×C19 | C22 |
| hypercenter | C2×C4 | D3×D19 |
| hypocenter | C3×C19 | #121 |
| LCS | G ▷ C22×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D228 | C2 | semidirect |
| 2. C2×C4×D3×C19 | C2 | semidirect |
| 3. C2×#90697 | C2 | semidirect |
| 4. C3×C4⋊Dic19 | C2 | semidirect |
| 5. #11744833 | C2 | semidirect |
| 19. C4⋊Dic19 | D3 | semidirect |
| 26. C2×D3×C19 | D4 | semidirect |
| 27. C3×C4×C19 | D4 | semidirect |
| 52. C4×C19 | D12 | semidirect |
| 54. C3×C19 | #121 | semidirect |
| 57. C2×C4×D3 | D19 | semidirect |
| 74. C19 | #895 | semidirect |
| 86. C2×D3 | D76 | semidirect |
| 88. C3×C4 | C22⋊D19 | semidirect |
| 112. C4 | #90697 | semidirect |
| 113. C3 | #10597376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D228 | 2 |
| C2×C4×D3×C19 | 2 |
| C2×#90697 | 2 |
| C3×C4⋊Dic19 | 2 |
| #11744833 | 2 |
| #10597376 | 3 |
| #895 | 19 |