Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 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⋊(D13⋊#3862) |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×C13⋊#3862 | 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. C72×Dic39 | C3 | semidirect |
| 4. C3×C13⋊#3862 | C4 | semidirect |
| 11. C3×C72×C13 | C3×C4 | semidirect |
| 13. C13⋊#3862 | Dic3 | semidirect |
| 19. C7×Dic39 | ΓL(1,𝔽8) | semidirect |
| 20. C7×Dic39 | ΓL(1,𝔽8) | semidirect |
| 26. C72×C13 | C3×Dic3 | semidirect |
| 45. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 46. C3×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 58. Dic39 | #3862 | semidirect |
| 60. C3×C72 | Dic13⋊C3 | semidirect |
| 68. C7×C13 | Dic3×ΓL(1,𝔽8) | semidirect |
| 69. C7×C13 | Dic3×ΓL(1,𝔽8) | semidirect |
| 81. C72 | C3⋊(Dic13⋊C3) | semidirect |
| 89. C3×C13 | C4×#3862 | semidirect |
| 98. C3×C7 | #11763957 | semidirect |
| 99. C3×C7 | #11763958 | semidirect |
| 108. C13 | Dic3×#3862 | semidirect |
| 113. C7 | C3⋊#11763958 | semidirect |
| 114. C7 | C3⋊#11763957 | semidirect |
| 121. C3 | Dic13⋊#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C13⋊#3862 | 2 |
| C72×Dic39 | 3 |
| Dic13⋊#3862 | 3 |
| C3⋊#11763957 | 7 |
| C3⋊#11763958 | 7 |
| Dic3×#3862 | 13 |