Finite Group DatabasebetaFinite Group DatabasebetaOrder 22050.
152 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 21 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, cosocle, hypocenter | C3×C52×C72 | C2×C3 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C52⋊#3861 | C2 | semidirect |
| 2. C7×C3⋊(C5⋊D35) | C3 | semidirect |
| 5. C52⋊#3861 | D3 | semidirect |
| 6. C3×C52×C72 | C2×C3 | semidirect |
| 14. C52×C72 | C3×D3 | semidirect |
| 15. C3⋊(C5⋊D35) | ΓL(1,𝔽8) | semidirect |
| 22. C3×C52×C7 | AGL(1,𝔽7) | semidirect |
| 23. C3×C52×C7 | C2×ΓL(1,𝔽8) | semidirect |
| 42. C52×C7 | D3×ΓL(1,𝔽8) | semidirect |
| 43. C52×C7 | C3⋊AGL(1,𝔽7) | semidirect |
| 46. C3×C72 | (C5⋊D5)⋊C3 | semidirect |
| 55. C3×C52 | #64423 | semidirect |
| 64. C72 | C3⋊((C5⋊D5)⋊C3) | semidirect |
| 73. C52 | C3⋊#64423 | semidirect |
| 75. C3×C7 | (C5⋊D5)⋊ΓL(1,𝔽8) | semidirect |
| 76. C3×C7 | #11760386 | semidirect |
| 90. C7 | C3⋊#11760386 | semidirect |
| 91. C7 | C3⋊((C5⋊D5)⋊ΓL(1,𝔽8)) | semidirect |
| 97. C3 | #20301293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C52⋊#3861 | 2 |
| C7×C3⋊(C5⋊D35) | 3 |
| #20301293 | 3 |
| C3⋊((C5⋊D5)⋊ΓL(1,𝔽8)) | 7 |
| C3⋊#11760386 | 7 |
| C3⋊#64423 | 25 |