Finite Group DatabasebetaFinite Group DatabasebetaOrder 30492.
136 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 20 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. C7×C3⋊((C11⋊D11)⋊C3) | C2 | semidirect |
| 3. C3×C7⋊#10624391 | C2 | semidirect |
| 6. C3×C7×C112⋊C3 | C22 | semidirect |
| 8. C7×C3⋊(C11⋊D11) | D3 | semidirect |
| 12. C7⋊#10624391 | D3 | semidirect |
| 17. C7×C112⋊C3 | C2×D3 | semidirect |
| 18. C3×C7×C112 | C2×D3 | semidirect |
| 19. C3⋊((C11⋊D11)⋊C3) | D7 | semidirect |
| 27. C3×C112⋊C3 | C2×D7 | semidirect |
| 30. C7×C112 | D32 | semidirect |
| 31. C3⋊(C11⋊D11) | D21 | semidirect |
| 46. C3×C112 | C2×D21 | semidirect |
| 48. C112⋊C3 | D3×D7 | semidirect |
| 70. C112 | D3×D21 | semidirect |
| 107. C3×C7 | #10624391⋊C2 | semidirect |
| 120. C7 | #10624391⋊D3 | semidirect |
| 131. 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 |
| C7×C3⋊((C11⋊D11)⋊C3) | 2 |
| C3×C7⋊#10624391 | 2 |
| D77⋊D33 | 3 |
| ((C11⋊D11)⋊C3)⋊D7 | 3 |
| #10624391⋊D3 | 7 |
| D3×D21 | 121 |