Finite Group DatabasebetaFinite Group DatabasebetaOrder 30492.
180 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C9×C112 | C22 |
| Frattini | C3 | D33×D77 |
| socle | C3×C7×C112 | C2×D3 |
| LCS | G ▷ C7×C9×C112 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7⋊(C9⋊(C11⋊D11)) | C2 | semidirect |
| 2. C7×C11×D99 | C2 | semidirect |
| 3. C9×C11×D77 | C2 | semidirect |
| 5. C7×C9×C112 | C22 | semidirect |
| 15. C11×D99 | D7 | semidirect |
| 18. C11×D77 | D9 | semidirect |
| 24. C7×D99 | D11 | semidirect |
| 26. C9×D77 | D11 | semidirect |
| 28. C9×C112 | C2×D7 | semidirect |
| 31. C7×C112 | C2×D9 | semidirect |
| 36. C7×C9×C11 | C2×D11 | semidirect |
| 37. C7×C9×C11 | C2×D11 | semidirect |
| 62. D99 | D77 | direct (N × H) |
| 69. D77 | D99 | direct (N × H) |
| 77. C112 | D7×D9 | semidirect |
| 79. C9×C11 | D7×D11 | semidirect |
| 80. C9×C11 | C2×D77 | semidirect |
| 83. C7×C11 | D9×D11 | semidirect |
| 84. C7×C11 | C2×D99 | semidirect |
| 92. C7×C9 | D112 | semidirect |
| 119. C11 | D7×D99 | semidirect |
| 120. C11 | D9×D77 | semidirect |
| 121. C9 | D11×D77 | semidirect |
| 122. C7 | D11×D99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7⋊(C9⋊(C11⋊D11)) | 2 |
| C7×C11×D99 | 2 |
| C9×C11×D77 | 2 |
| D33×D77 | 3 |
| D11×D99 | 7 |
| D9×D77 | 11 |
| D7×D99 | 11 |