Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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 | C2 | C3⋊#16838471 |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×C7×#63271 | C2 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×C3⋊(C7⋊Dic7) | C3 | semidirect |
| 4. C3×C7×#63271 | C4 | semidirect |
| 11. C3×C72×C13 | C3×C4 | semidirect |
| 13. C7×#63271 | Dic3 | semidirect |
| 24. C3×#63271 | Dic7 | semidirect |
| 26. C72×C13 | C3×Dic3 | semidirect |
| 27. C3⋊(C7⋊Dic7) | C13⋊C3 | semidirect |
| 45. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 46. C3×C7×C13 | C3×Dic7 | semidirect |
| 48. #63271 | Dic21 | semidirect |
| 60. C3×C72 | C4×C13⋊C3 | semidirect |
| 68. C7×C13 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 69. C7×C13 | C3×Dic21 | semidirect |
| 81. C72 | Dic3×C13⋊C3 | semidirect |
| 89. C3×C13 | ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 100. C3×C7 | Dic7×C13⋊C3 | semidirect |
| 101. C3×C7 | #11763962 | semidirect |
| 108. C13 | C3⋊(ΓL(1,𝔽8)⋊Dic7) | semidirect |
| 113. C7 | C13⋊C3×Dic21 | semidirect |
| 114. C7 | C3⋊#11763962 | semidirect |
| 121. C3 | #21439547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#63271 | 2 |
| C13×C3⋊(C7⋊Dic7) | 3 |
| #21439547 | 3 |
| C3⋊#11763962 | 7 |
| C13⋊C3×Dic21 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic7) | 13 |