Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
184 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 41 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⋊#16838458 |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×#14274263 | 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. C7×C13×Dic21 | C3 | semidirect |
| 4. C3×#14274263 | C4 | semidirect |
| 11. C3×C72×C13 | C3×C4 | semidirect |
| 13. #14274263 | Dic3 | semidirect |
| 19. C13×Dic21 | ΓL(1,𝔽8) | semidirect |
| 27. C72×C13 | C3×Dic3 | semidirect |
| 28. C7×Dic21 | C13⋊C3 | semidirect |
| 47. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 48. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 64. C3×C72 | C4×C13⋊C3 | semidirect |
| 73. C7×C13 | Dic3×ΓL(1,𝔽8) | semidirect |
| 74. C7×C13 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 75. Dic21 | #63270 | semidirect |
| 86. C72 | Dic3×C13⋊C3 | semidirect |
| 96. C3×C13 | #10596873 | semidirect |
| 104. C3×C7 | #11763961 | semidirect |
| 105. C3×C7 | C4×#63270 | semidirect |
| 116. C13 | C3⋊#10596873 | semidirect |
| 121. C7 | Dic3×#63270 | semidirect |
| 122. C7 | C3⋊#11763961 | semidirect |
| 129. C3 | #21439534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#14274263 | 2 |
| C7×C13×Dic21 | 3 |
| #21439534 | 3 |
| C3⋊#11763961 | 7 |
| Dic3×#63270 | 7 |
| C3⋊#10596873 | 13 |