Finite Group DatabasebetaFinite Group Databasebeta← ((C11⋊D11)⋊C3)⋊D21 #44479124
Order 30492.
168 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 31 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, cosocle, hypocenter | C3×C7×C112⋊C3 | C22 |
| Fitting, socle | C3×C7×C112 | C2×D3 |
| LCS | G ▷ C3×C7×C112⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C7⋊#10624391) | C2 | semidirect |
| 2. C3⋊(C7⋊#10624391) | C2 | semidirect |
| 3. C3×C7×(C11⋊D11)⋊C3 | C2 | semidirect |
| 7. C3×C7×C112⋊C3 | C22 | semidirect |
| 10. C3×C7×C11⋊D11 | D3 | semidirect |
| 15. C7×(C11⋊D11)⋊C3 | D3 | semidirect |
| 16. C7×(C11⋊D11)⋊C3 | D3 | semidirect |
| 19. C7×C112⋊C3 | C2×D3 | semidirect |
| 20. C7×C112⋊C3 | C2×D3 | semidirect |
| 21. C3×C7×C112 | C2×D3 | semidirect |
| 24. C3×(C11⋊D11)⋊C3 | D7 | semidirect |
| 27. C7×C11⋊D11 | C3⋊D3 | semidirect |
| 31. C3×C112⋊C3 | C2×D7 | semidirect |
| 34. C7×C112 | C2×C3⋊D3 | semidirect |
| 37. C3×C11⋊D11 | D21 | semidirect |
| 38. (C11⋊D11)⋊C3 | D21 | semidirect |
| 39. (C11⋊D11)⋊C3 | D21 | semidirect |
| 52. C3×C112 | C2×D21 | semidirect |
| 53. C112⋊C3 | C2×D21 | semidirect |
| 54. C112⋊C3 | C2×D21 | semidirect |
| 58. C11⋊D11 | C3⋊D21 | semidirect |
| 76. C112 | C2×C3⋊D21 | semidirect |
| 116. C3×C7 | #10624391⋊C2 | semidirect |
| 130. C7 | ((C11⋊D11)⋊C3)⋊D3 | semidirect |
| 143. C3 | ((C11⋊D11)⋊C3)⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C7⋊#10624391) | 2 |
| C3×C7×(C11⋊D11)⋊C3 | 2 |
| #23779059 | 3 |
| ((C11⋊D11)⋊C3)⋊D7 | 3 |
| ((C11⋊D11)⋊C3)⋊D3 | 7 |
| C2×C3⋊D21 | 121 |