Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
280 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 122 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⋊((C13⋊C3)⋊(C7⋊D7)) |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×C72×C13⋊C3 | 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. C3⋊(C7⋊Dic91) | C3 | semidirect |
| 4. C3×C72×C13⋊C3 | C4 | semidirect |
| 11. C3×C72×C13 | C3×C4 | semidirect |
| 13. C72×C13⋊C3 | Dic3 | semidirect |
| 23. C3×C7×C13⋊C3 | Dic7 | semidirect |
| 24. C3×C7×C13⋊C3 | Dic7 | semidirect |
| 25. C72×C13 | C3×Dic3 | semidirect |
| 41. C3×C7×C13 | C3×Dic7 | semidirect |
| 42. C3×C7×C13 | C3×Dic7 | semidirect |
| 45. C7×C13⋊C3 | Dic21 | semidirect |
| 46. C7×C13⋊C3 | Dic21 | semidirect |
| 57. C3×C72 | Dic13⋊C3 | semidirect |
| 60. C3×C13⋊C3 | C7⋊Dic7 | semidirect |
| 62. C7×C13 | C3×Dic21 | semidirect |
| 63. C7×C13 | C3×Dic21 | semidirect |
| 74. C72 | C3⋊(Dic13⋊C3) | semidirect |
| 81. C3×C13 | C3×C7⋊Dic7 | semidirect |
| 83. C13⋊C3 | C3⋊(C7⋊Dic7) | semidirect |
| 92. C3×C7 | #11763955 | semidirect |
| 93. C3×C7 | #11763955 | semidirect |
| 97. C13 | C3×C3⋊(C7⋊Dic7) | semidirect |
| 101. C7 | C3⋊#11763955 | semidirect |
| 102. C7 | C3⋊#11763955 | semidirect |
| 109. C3 | #21439560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C72×C13⋊C3 | 2 |
| C3⋊(C7⋊Dic91) | 3 |
| #21439560 | 3 |
| C3⋊#11763955 | 7 |
| C3×C3⋊(C7⋊Dic7) | 13 |