Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
128 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 47 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 | C3 | D7×#11716321 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C22×C3 |
| prime radical | C3×C7×D7×D19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D7×#11924776 | C2 | semidirect |
| 2. #30660605 | C2 | semidirect |
| 3. C7×#14558780 | C2 | semidirect |
| 5. C7×#11924776 | C22 | semidirect |
| 11. C7×D7×D19 | C9 | semidirect |
| 15. #14558780 | D7 | direct (N × H) |
| 19. C7×D133 | C2×C9 | semidirect |
| 20. C7×D7×C19 | C2×C9 | semidirect |
| 21. C72×D19 | C2×C9 | semidirect |
| 25. #11924776 | C2×D7 | semidirect |
| 27. C72×C19 | C22×C9 | semidirect |
| 41. D7×D19 | C7⋊C9 | semidirect |
| 53. D133 | C2×C7⋊C9 | semidirect |
| 56. C7×D19 | C2×C7⋊C9 | semidirect |
| 57. C7×D19 | C9×D7 | semidirect |
| 58. D7×C19 | C2×C7⋊C9 | semidirect |
| 66. C7×C19 | C22×C7⋊C9 | semidirect |
| 67. C7×C19 | C2×C9×D7 | semidirect |
| 79. C7×D7 | #4294⋊C2 | semidirect |
| 86. C72 | C2×#4294⋊C2 | semidirect |
| 96. D19 | D7×C7⋊C9 | semidirect |
| 103. C19 | C2×D7×C7⋊C9 | semidirect |
| 113. D7 | #14558780 | direct (N × H) |
| 117. C7 | D7×#4294⋊C2 | semidirect |
| 118. C7 | C2×#14558780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#11924776 | 2 |
| #30660605 | 2 |
| C7×#14558780 | 2 |
| C3×C7×D7×D19 | 3 |
| C2×#14558780 | 7 |
| D7×#4294⋊C2 | 7 |
| C2×D7×C7⋊C9 | 19 |