Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
184 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 33 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, hypocenter | C3×C72×C17 | C3×C4 |
| prime radical | C3×D17×#3861 | C2 |
| cosocle | C3×C72×D17 | C2×C3 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C3⋊(C7⋊#595) | C3 | semidirect |
| 4. C3×C17×#3861 | C4 | semidirect |
| 12. C17×#3861 | Dic3 | semidirect |
| 13. C3×C72×C17 | C3×C4 | semidirect |
| 19. C3⋊(C7⋊#595) | ΓL(1,𝔽8) | semidirect |
| 27. C72×C17 | C3×Dic3 | semidirect |
| 42. C3×#3861 | #595 | semidirect |
| 44. C3×C7×C17 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 45. C3×C7×C17 | C4×ΓL(1,𝔽8) | semidirect |
| 65. C3×C72 | C3×#595 | semidirect |
| 67. #3861 | C3⋊#595 | semidirect |
| 72. C7×C17 | Dic3×ΓL(1,𝔽8) | semidirect |
| 73. C7×C17 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 88. C3×C17 | #10596873 | semidirect |
| 89. C72 | C3×C3⋊#595 | semidirect |
| 104. C3×C7 | ΓL(1,𝔽8)×#595 | semidirect |
| 105. C3×C7 | ΓL(1,𝔽8)⋊#595 | semidirect |
| 113. C17 | C3⋊#10596873 | semidirect |
| 121. C7 | C3⋊(ΓL(1,𝔽8)⋊#595) | semidirect |
| 122. C7 | ΓL(1,𝔽8)×C3⋊#595 | semidirect |
| 129. C3 | #23756186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D17×#3861 | 2 |
| C7×C3⋊(C7⋊#595) | 3 |
| #23756186 | 3 |
| ΓL(1,𝔽8)×C3⋊#595 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊#595) | 7 |
| C3⋊#10596873 | 17 |