Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
346 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72276832 | C2 | semidirect |
| 2. #72276825 | C2 | semidirect |
| 3. D3×#10597167 | C2 | semidirect |
| 5. D3×AGL(1,𝔽25) | C2 | semidirect |
| 7. #72276706 | C2 | semidirect |
| 8. C3×AΓL(1,𝔽25) | C2 | semidirect |
| 17. C3⋊AGL(1,𝔽25) | C22 | semidirect |
| 18. C3×AGL(1,𝔽25) | C22 | semidirect |
| 19. C3⋊#10597167 | C22 | semidirect |
| 20. C3×#10597167 | C22 | semidirect |
| 27. D3×#6053 | D3 | semidirect |
| 35. AΓL(1,𝔽25) | D3 | direct (N × H) |
| 54. C3⋊#6053 | C2×D3 | semidirect |
| 56. C3×#6053 | C2×D3 | semidirect |
| 67. AGL(1,𝔽25) | C2×D3 | semidirect |
| 70. #10597167 | C2×D3 | semidirect |
| 71. C3⋊((C5⋊D5)⋊C3) | M16 | semidirect |
| 72. D3×C52⋊C3 | M16 | semidirect |
| 106. C3×C52⋊C3 | C2×M16 | semidirect |
| 117. #6053 | D32 | semidirect |
| 118. C3⋊(C5⋊D5) | ΓL(1,𝔽25) | semidirect |
| 120. C52×D3 | ΓL(1,𝔽25) | semidirect |
| 156. C3×C52 | C2×ΓL(1,𝔽25) | semidirect |
| 158. C52⋊C3 | D3×M16 | semidirect |
| 225. C52 | D3×ΓL(1,𝔽25) | semidirect |
| 326. D3 | AΓL(1,𝔽25) | direct (N × H) |
| 339. C3 | C2×AΓL(1,𝔽25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72276832 | 2 |
| #72276825 | 2 |
| D3×#10597167 | 2 |
| D3×#64480⋊C2 | 2 |
| D3×AGL(1,𝔽25) | 2 |
| D3×#6053⋊C2 | 3 |
| #72276706 | 2 |
| C3×AΓL(1,𝔽25) | 2 |
| C2×AΓL(1,𝔽25) | 3 |
| D3×ΓL(1,𝔽25) | 25 |