Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
112 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 49 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 | C22×D57 |
| commutator, socle, prime radical, cosocle | C22×C3×C19 | C23 |
| Fitting | C3×C4⋊C4×C19 | C2 |
| hypercenter | C4⋊C4 | D57 |
| hypocenter | C3×C19 | #125 |
| LCS | G ▷ C22×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. C3×C19 | #125 | semidirect |
| 69. C19 | #889 | semidirect |
| 103. C3 | #10597335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊C4×C19 | 2 |
| C4⋊Dic57 | 2 |
| #11744887 | 2 |
| C4×Dic57 | 2 |
| #10597335 | 3 |
| #889 | 19 |