Finite Group DatabasebetaFinite Group DatabasebetaOrder 25284.
200 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 41 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 | C72×C43 | C22×C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D43×#3861 | C2 | semidirect |
| 2. #27162408 | C2 | semidirect |
| 3. C43×#64424 | C2 | semidirect |
| 4. D43×C7⋊D7 | C3 | semidirect |
| 5. C43×#3861 | C22 | semidirect |
| 6. C7⋊D301 | C2×C3 | semidirect |
| 7. C43×C7⋊D7 | C2×C3 | semidirect |
| 8. C72×D43 | C2×C3 | semidirect |
| 12. C72×C43 | C22×C3 | semidirect |
| 31. C7×D43 | AGL(1,𝔽7) | semidirect |
| 32. C7×D43 | AGL(1,𝔽7) | semidirect |
| 33. C7×D43 | AGL(1,𝔽7) | semidirect |
| 39. C7×C43 | C2×AGL(1,𝔽7) | semidirect |
| 40. C7×C43 | C2×AGL(1,𝔽7) | semidirect |
| 41. C7×C43 | C2×AGL(1,𝔽7) | semidirect |
| 44. #64424 | D43 | direct (N × H) |
| 50. #3861 | C2×D43 | semidirect |
| 54. C7⋊D7 | C3×D43 | semidirect |
| 57. D43 | #64424 | direct (N × H) |
| 61. C72 | C2×C3×D43 | semidirect |
| 62. C43 | C2×#64424 | semidirect |
| 88. C7 | AGL(1,𝔽7)×D43 | semidirect |
| 89. C7 | AGL(1,𝔽7)×D43 | semidirect |
| 90. C7 | AGL(1,𝔽7)×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D43×#3861 | 2 |
| #27162408 | 2 |
| C43×#64424 | 2 |
| D43×C7⋊D7 | 3 |
| AGL(1,𝔽7)×D43 | 7 |
| C2×#64424 | 43 |