Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
600 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #26013885 |
| commutator, cosocle, hypocenter | C72×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#19150312 | C2 | semidirect |
| 2. C3×#19150287 | C2 | semidirect |
| 3. C3×#19150285 | C2 | semidirect |
| 4. C3×D19×C7⋊D7 | C3 | semidirect |
| 5. #26013885 | C3 | direct (N × H) |
| 6. C3×#14584116 | C22 | semidirect |
| 7. C3×C7⋊D133 | C2×C3 | semidirect |
| 8. C3×C19×C7⋊D7 | C2×C3 | semidirect |
| 9. C3×C72×D19 | C2×C3 | semidirect |
| 10. #19150312 | C2×C3 | semidirect |
| 11. #19150287 | C2×C3 | semidirect |
| 12. #19150285 | C2×C3 | semidirect |
| 14. D19×C7⋊D7 | C32 | semidirect |
| 15. #14584116 | C22×C3 | semidirect |
| 16. C3×C72×C19 | C22×C3 | semidirect |
| 20. C7⋊D133 | C2×C32 | semidirect |
| 21. C19×C7⋊D7 | C2×C32 | semidirect |
| 22. C72×D19 | C2×C32 | semidirect |
| 27. C72×C19 | C22×C32 | semidirect |
| 33. C3×C7×D19 | AGL(1,𝔽7) | semidirect |
| 42. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 49. C3×C7⋊D7 | D19⋊C3 | semidirect |
| 54. C7×D19 | C3×AGL(1,𝔽7) | semidirect |
| 61. C3×C72 | C2×D19⋊C3 | semidirect |
| 63. C7×C19 | C2×C3×AGL(1,𝔽7) | semidirect |
| 69. C3×D19 | #64424 | semidirect |
| 75. C7⋊D7 | C3×D19⋊C3 | semidirect |
| 80. C3×C19 | C2×#64424 | semidirect |
| 82. C72 | C2×C3×D19⋊C3 | semidirect |
| 91. D19 | C3×#64424 | semidirect |
| 94. C3×C7 | #11716322⋊C2 | semidirect |
| 96. C19 | C2×C3×#64424 | semidirect |
| 106. C7 | C3×#11716322⋊C2 | semidirect |
| 115. C3 | #26013885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#19150312 | 2 |
| C3×#19150287 | 2 |
| C3×#19150285 | 2 |
| C3×D19×C7⋊D7 | 3 |
| #26013885 | 3 |
| C3×#11716322⋊C2 | 7 |
| C2×C3×#64424 | 19 |