Finite Group DatabasebetaFinite Group Databasebeta← C3×ΓL(1,𝔽8)×C7⋊#595 #44472748
Order 29988.
152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 2. C3×C7×C7⋊#595 | C3 | semidirect |
| 3. ΓL(1,𝔽8)×C7⋊#595 | C3 | direct (N × H) |
| 4. C3×C7×C17×ΓL(1,𝔽8) | C4 | semidirect |
| 9. C7×C7⋊#595 | C32 | semidirect |
| 10. C7×C17×ΓL(1,𝔽8) | C3×C4 | semidirect |
| 11. C3×C72×C17 | C3×C4 | semidirect |
| 17. C3×C7⋊#595 | ΓL(1,𝔽8) | direct (N × H) |
| 21. C3×C17×ΓL(1,𝔽8) | Dic7 | semidirect |
| 23. C72×C17 | C32×C4 | semidirect |
| 32. C7⋊#595 | C3×ΓL(1,𝔽8) | direct (N × H) |
| 34. C3×C7×ΓL(1,𝔽8) | #595 | semidirect |
| 37. C3×C7×C17 | C4×ΓL(1,𝔽8) | semidirect |
| 38. C3×C7×C17 | C3×Dic7 | semidirect |
| 39. C17×ΓL(1,𝔽8) | C3×Dic7 | semidirect |
| 52. C3×C72 | C3×#595 | semidirect |
| 53. C7×ΓL(1,𝔽8) | C3×#595 | semidirect |
| 57. C7×C17 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 58. C7×C17 | C32×Dic7 | semidirect |
| 68. C3×ΓL(1,𝔽8) | C7⋊#595 | direct (N × H) |
| 70. C3×C17 | ΓL(1,𝔽8)×Dic7 | semidirect |
| 71. C72 | C32×#595 | semidirect |
| 83. C3×C7 | ΓL(1,𝔽8)×#595 | semidirect |
| 84. C3×C7 | C3×C7⋊#595 | semidirect |
| 85. ΓL(1,𝔽8) | C3×C7⋊#595 | direct (N × H) |
| 87. C17 | C3×ΓL(1,𝔽8)×Dic7 | semidirect |
| 95. C7 | C3×ΓL(1,𝔽8)×#595 | semidirect |
| 96. C7 | C32×C7⋊#595 | semidirect |
| 101. C3 | ΓL(1,𝔽8)×C7⋊#595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×ΓL(1,𝔽8)×D17 | 2 |
| C3×C7×C7⋊#595 | 3 |
| ΓL(1,𝔽8)×C7⋊#595 | 3 |
| C32×C7⋊#595 | 7 |
| C3×ΓL(1,𝔽8)×#595 | 7 |
| C3×ΓL(1,𝔽8)×Dic7 | 17 |