Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
446 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757745 |
| commutator, cosocle, hypocenter | C3×C92 | C23 |
| Frattini | C32 | C2×#1113 |
| Fitting | C2×C3×C92 | C22 |
| socle | C2×C33 | D32 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C9⋊D9 | C2 | semidirect |
| 2. C2×C9×C3⋊D9 | C2 | semidirect |
| 3. #11757745 | C2 | direct (N × H) |
| 6. C2×C3×C92 | C22 | semidirect |
| 7. C3×C9⋊D9 | C22 | semidirect |
| 8. C9×C3⋊D9 | C22 | semidirect |
| 14. C2×C9⋊D9 | D3 | semidirect |
| 18. C3×C92 | C23 | semidirect |
| 30. C2×C92 | C2×D3 | semidirect |
| 31. C9⋊D9 | C2×D3 | semidirect |
| 39. C2×C3⋊D9 | D9 | semidirect |
| 54. C92 | C22×D3 | semidirect |
| 69. C2×C3×C9 | C2×D9 | semidirect |
| 73. C3⋊D9 | C2×D9 | semidirect |
| 107. C3×C9 | C22×D9 | semidirect |
| 129. C2×C9 | D3×D9 | semidirect |
| 154. C9 | C2×D3×D9 | semidirect |
| 161. C2×C3 | D92 | semidirect |
| 174. C3 | C2×D92 | semidirect |
| 178. C2 | #11757745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9⋊D9 | 2 |
| C2×C9×C3⋊D9 | 2 |
| #11757745 | 2 |
| C2×#66431 | 3 |
| C2×D92 | 3 |