Finite Group DatabasebetaFinite Group Databasebeta← #3861⋊(C22⋊(C13⋊C3)) #37525404
Order 22932.
152 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 26 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, cosocle, hypocenter | C22×C72×C13 | C32 |
| LCS | G ▷ C22×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×#3861 | C3 | semidirect |
| 2. C7×C22⋊#63271 | C3 | semidirect |
| 3. C7×C22⋊#63270 | C3 | semidirect |
| 4. C22⋊(C13⋊#3862) | C3 | semidirect |
| 9. C22×C72×C13 | C32 | semidirect |
| 11. C13×#3861 | A4 | semidirect |
| 17. C22⋊#63270 | ΓL(1,𝔽8) | semidirect |
| 19. C22⋊#63271 | ΓL(1,𝔽8) | semidirect |
| 27. C72×C13 | C3×A4 | semidirect |
| 31. C22×#3861 | C13⋊C3 | semidirect |
| 38. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 39. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 52. C22×C72 | C3×C13⋊C3 | semidirect |
| 61. #3861 | C22⋊(C13⋊C3) | semidirect |
| 67. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 68. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 81. C22×C13 | ΓL(1,𝔽8)2 | semidirect |
| 82. C72 | C3×C22⋊(C13⋊C3) | semidirect |
| 92. C22×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 93. C22×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 107. C13 | #3861⋊A4 | semidirect |
| 114. C7 | ΓL(1,𝔽8)×C22⋊(C13⋊C3) | semidirect |
| 115. C7 | ΓL(1,𝔽8)×C22⋊(C13⋊C3) | semidirect |
| 117. C22 | #3861⋊(C13⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#3861 | 3 |
| C7×C22⋊#63271 | 3 |
| C7×C22⋊#63270 | 3 |
| C22⋊(C13⋊#3862) | 3 |
| #3861⋊(C13⋊C3) | 4 |
| ΓL(1,𝔽8)×C22⋊(C13⋊C3) | 7 |
| #3861⋊A4 | 13 |