Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 188 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.
| 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×C3×D76 | C2 | semidirect |
| 2. C2×#90696 | C2 | semidirect |
| 3. C2×#90696 | C2 | semidirect |
| 4. C2×Dic3×D19 | C2 | semidirect |
| 5. #11744889 | C2 | semidirect |
| 6. C19×Dic3⋊C4 | C2 | semidirect |
| 7. (C2×D19)⋊Dic3 | C2 | semidirect |
| 22. C2×D76 | D3 | semidirect |
| 36. C2×C3×D19 | D4 | semidirect |
| 40. Dic3×C19 | D4 | semidirect |
| 68. C2×D19 | #67 | semidirect |
| 73. C3×C19 | #121 | semidirect |
| 80. Dic3⋊C4 | D19 | semidirect |
| 99. C19 | #939 | semidirect |
| 120. Dic3 | D76 | semidirect |
| 152. C3 | #10597341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D76 | 2 |
| C2×#90696 | 2 |
| C2×Dic3×D19 | 2 |
| #11744889 | 2 |
| C19×Dic3⋊C4 | 2 |
| (C2×D19)⋊Dic3 | 2 |
| #10597341 | 3 |
| #939 | 19 |