Finite Group DatabasebetaFinite Group Databasebeta← C3×(C3×ΓL(1,𝔽8))⋊H(3,𝔽3) #19103151
Order 5103.
3824 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 3824 conjugacy classes of subgroups — too many to draw. Only its 382 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. C34×ΓL(1,𝔽8) | C3 | semidirect |
| 2. C32×C7⋊H(3,𝔽3) | C3 | semidirect |
| 3. C32×C7⋊H(3,𝔽3) | C3 | semidirect |
| 4. (C3×ΓL(1,𝔽8))⋊H(3,𝔽3) | C3 | direct (N × H) |
| 5. C32×C7×H(3,𝔽3) | C3 | semidirect |
| 8. C34×C7 | C32 | semidirect |
| 12. C33×ΓL(1,𝔽8) | C32 | semidirect |
| 13. C33×ΓL(1,𝔽8) | C32 | semidirect |
| 15. C3×C7×H(3,𝔽3) | C32 | semidirect |
| 18. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 19. C3×C7⋊H(3,𝔽3) | C32 | semidirect |
| 23. C32×H(3,𝔽3) | ΓL(1,𝔽8) | semidirect |
| 28. C33×C7 | H(3,𝔽3) | semidirect |
| 31. C33×C7 | C33 | semidirect |
| 39. C32×ΓL(1,𝔽8) | H(3,𝔽3) | semidirect |
| 41. C32×ΓL(1,𝔽8) | C33 | semidirect |
| 51. C34 | C3×ΓL(1,𝔽8) | semidirect |
| 57. C3×H(3,𝔽3) | C3×ΓL(1,𝔽8) | semidirect |
| 65. C32×C7 | C3×H(3,𝔽3) | semidirect |
| 74. C3×ΓL(1,𝔽8) | C3×H(3,𝔽3) | semidirect |
| 88. C33 | C7⋊H(3,𝔽3) | semidirect |
| 91. C33 | C32×ΓL(1,𝔽8) | semidirect |
| 97. C3×C7 | C32⋊H(3,𝔽3) | semidirect |
| 117. C32 | C3×C7⋊H(3,𝔽3) | semidirect |
| 119. C7 | C3×C32⋊H(3,𝔽3) | semidirect |
| 124. C3 | (C3×ΓL(1,𝔽8))⋊H(3,𝔽3) | direct (N × H) |