Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #30660717 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical | C2×C7×(C19⋊C3)⋊D7 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#11924781 | C2 | semidirect |
| 2. #30660717 | C2 | direct (N × H) |
| 4. C7×#11924781 | C22 | semidirect |
| 9. C2×C7×D133 | C9 | semidirect |
| 11. C2×#11924781 | D7 | semidirect |
| 15. C2×C72×C19 | C2×C9 | semidirect |
| 16. C7×D133 | C2×C9 | semidirect |
| 20. #11924781 | C2×D7 | semidirect |
| 22. C72×C19 | C22×C9 | semidirect |
| 32. C2×D133 | C7⋊C9 | semidirect |
| 43. C2×C7×C19 | C2×C7⋊C9 | semidirect |
| 44. C2×C7×C19 | C9×D7 | semidirect |
| 45. D133 | C2×C7⋊C9 | semidirect |
| 54. C7×C19 | C22×C7⋊C9 | semidirect |
| 55. C7×C19 | C2×C9×D7 | semidirect |
| 62. C2×C72 | AGL(1,𝔽19) | semidirect |
| 70. C72 | C2×AGL(1,𝔽19) | semidirect |
| 76. C2×C19 | D7×C7⋊C9 | semidirect |
| 84. C19 | C2×D7×C7⋊C9 | semidirect |
| 89. C2×C7 | #14558808 | semidirect |
| 90. C2×C7 | #4296⋊D7 | semidirect |
| 95. C7 | C2×#14558808 | semidirect |
| 96. C7 | C2×#4296⋊D7 | semidirect |
| 102. C2 | #30660717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#11924781 | 2 |
| #30660717 | 2 |
| C2×C7×(C19⋊C3)⋊D7 | 3 |
| C2×#4296⋊D7 | 7 |
| C2×#14558808 | 7 |
| C2×D7×C7⋊C9 | 19 |