Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#14584116 | C2 | semidirect |
| 2. C3⋊#19150285 | C2 | semidirect |
| 3. C3×#19150285 | C2 | semidirect |
| 4. D3×C7⋊D133 | C3 | semidirect |
| 6. C3×#14584116 | C22 | semidirect |
| 7. C3⋊(C7⋊D133) | C2×C3 | semidirect |
| 8. D3×C72×C19 | C2×C3 | semidirect |
| 9. C3×C7⋊D133 | C2×C3 | semidirect |
| 13. #19150285 | D3 | direct (N × H) |
| 17. #14584116 | C2×D3 | semidirect |
| 18. C3×C72×C19 | C22×C3 | semidirect |
| 24. C7⋊D133 | C3×D3 | semidirect |
| 29. C72×C19 | C2×C3×D3 | semidirect |
| 34. D3×C7×C19 | AGL(1,𝔽7) | semidirect |
| 45. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 52. D3×C72 | D19⋊C3 | semidirect |
| 66. C3×C72 | C2×D19⋊C3 | semidirect |
| 69. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 75. D3×C19 | #64424 | semidirect |
| 87. C3×C19 | C2×#64424 | semidirect |
| 90. C72 | D3×D19⋊C3 | semidirect |
| 93. D3×C7 | #11716328 | semidirect |
| 103. C3×C7 | C2×#11716328 | semidirect |
| 106. C19 | D3×#64424 | semidirect |
| 116. C7 | D3×#11716328 | semidirect |
| 123. D3 | #19150285 | direct (N × H) |
| 127. C3 | C2×#19150285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#14584116 | 2 |
| C3⋊#19150285 | 2 |
| C3×#19150285 | 2 |
| D3×C7⋊D133 | 3 |
| C2×#19150285 | 3 |
| D3×#11716328 | 7 |
| D3×#64424 | 19 |