Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
160 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 34 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, hypocenter | C72×C19 | C22×C9 |
| prime radical | C7⋊D7×D19⋊C3 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660702 | C2 | semidirect |
| 2. #30660700 | C2 | semidirect |
| 3. C7×#14558808 | C2 | semidirect |
| 5. C7×#11924781 | C22 | semidirect |
| 11. D19×C7⋊D7 | C9 | semidirect |
| 15. #14558808 | D7 | semidirect |
| 19. C7⋊D133 | C2×C9 | semidirect |
| 20. C19×C7⋊D7 | C2×C9 | semidirect |
| 21. C72×D19 | C2×C9 | semidirect |
| 26. #11924781 | C2×D7 | semidirect |
| 28. C72×C19 | C22×C9 | semidirect |
| 60. C7×D19 | D7⋊C9 | semidirect |
| 61. C7×D19 | C9×D7 | semidirect |
| 72. C7×C19 | C2×D7⋊C9 | semidirect |
| 73. C7×C19 | C2×C9×D7 | semidirect |
| 85. C7⋊D7 | AGL(1,𝔽19) | semidirect |
| 93. C72 | C2×AGL(1,𝔽19) | semidirect |
| 105. D19 | (C7⋊C9)⋊D7 | semidirect |
| 113. C19 | C2×(C7⋊C9)⋊D7 | semidirect |
| 129. C7 | #14558802⋊C2 | semidirect |
| 130. C7 | D7×AGL(1,𝔽19) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660702 | 2 |
| #30660700 | 2 |
| C7×#14558808 | 2 |
| C7⋊D7×D19⋊C3 | 3 |
| D7×AGL(1,𝔽19) | 7 |
| #14558802⋊C2 | 7 |
| C2×(C7⋊C9)⋊D7 | 19 |