Finite Group DatabasebetaFinite Group DatabasebetaOrder 32634.
100 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 28 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×C37 | C2×C32 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37⋊C3×#3862 | C2 | semidirect |
| 2. #24925966 | C3 | semidirect |
| 3. #24925965 | C3 | semidirect |
| 4. C37×#64422 | C3 | semidirect |
| 5. C7×D7×C37⋊C3 | C3 | semidirect |
| 6. C37⋊#3862 | C2×C3 | semidirect |
| 7. C37⋊#3862 | C2×C3 | semidirect |
| 8. C37×#3862 | C2×C3 | semidirect |
| 9. C72×C37⋊C3 | C2×C3 | semidirect |
| 12. C7×D7×C37 | C32 | semidirect |
| 15. C72×C37 | C2×C32 | semidirect |
| 23. D7×C37⋊C3 | ΓL(1,𝔽8) | semidirect |
| 30. C7×C37⋊C3 | AGL(1,𝔽7) | semidirect |
| 31. C7×C37⋊C3 | C2×ΓL(1,𝔽8) | semidirect |
| 36. D7×C37 | C3×ΓL(1,𝔽8) | semidirect |
| 42. #64422 | C37⋊C3 | direct (N × H) |
| 44. C7×C37 | C3×AGL(1,𝔽7) | semidirect |
| 45. C7×C37 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 53. #3862 | C2×C37⋊C3 | semidirect |
| 59. C37⋊C3 | #64422 | direct (N × H) |
| 60. C7×D7 | C3×C37⋊C3 | semidirect |
| 64. C72 | C2×C3×C37⋊C3 | semidirect |
| 73. C37 | C3×#64422 | semidirect |
| 85. D7 | ΓL(1,𝔽8)×C37⋊C3 | semidirect |
| 88. C7 | AGL(1,𝔽7)×C37⋊C3 | semidirect |
| 89. C7 | C2×ΓL(1,𝔽8)×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37⋊C3×#3862 | 2 |
| #24925966 | 3 |
| #24925965 | 3 |
| C37×#64422 | 3 |
| C7×D7×C37⋊C3 | 3 |
| C2×ΓL(1,𝔽8)×C37⋊C3 | 7 |
| AGL(1,𝔽7)×C37⋊C3 | 7 |
| C3×#64422 | 37 |