Finite Group DatabasebetaFinite Group DatabasebetaOrder 35700.
120 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 120 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 | C7×C17×C52⋊C3 | C22 |
| Fitting, socle | C52×C7×C17 | C2×D3 |
| LCS | G ▷ C7×C17×C52⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C17⋊((C5⋊D5)⋊C3) | C2 | semidirect |
| 2. C7⋊(C17⋊#3874) | C2 | semidirect |
| 3. C17×C7⋊#3874 | C2 | semidirect |
| 5. C7×C17×C52⋊C3 | C22 | semidirect |
| 6. C7×C5⋊D85 | D3 | semidirect |
| 10. C52×C7×C17 | C2×D3 | semidirect |
| 11. C17⋊((C5⋊D5)⋊C3) | D7 | semidirect |
| 19. C17×C52⋊C3 | C2×D7 | semidirect |
| 28. C7⋊#3874 | D17 | semidirect |
| 29. C5⋊D85 | D21 | semidirect |
| 38. C7×C52⋊C3 | C2×D17 | semidirect |
| 40. C52×C17 | C2×D21 | semidirect |
| 52. C52×C7 | D3×D17 | semidirect |
| 64. C7×C17 | #3874⋊C2 | semidirect |
| 72. C52⋊C3 | D7×D17 | semidirect |
| 93. C52 | D17×D21 | semidirect |
| 97. C17 | ((C5⋊D5)⋊C3)⋊D7 | semidirect |
| 108. C7 | #3874⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C17⋊((C5⋊D5)⋊C3) | 2 |
| C7⋊(C17⋊#3874) | 2 |
| C17×C7⋊#3874 | 2 |
| D35⋊D85 | 3 |
| #3874⋊D17 | 7 |
| ((C5⋊D5)⋊C3)⋊D7 | 17 |
| D17×D21 | 25 |