Finite Group DatabasebetaFinite Group Databasebeta← #3862×C22⋊(C13⋊C3) #37525424
Order 22932.
132 conjugacy classes of subgroups.
| 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×#3862 | C3 | semidirect |
| 2. C72×C22⋊(C13⋊C3) | C3 | semidirect |
| 3. C22⋊(C13⋊#3862) | C3 | semidirect |
| 7. C22×C72×C13 | C32 | semidirect |
| 9. C13×#3862 | A4 | semidirect |
| 16. C7×C22⋊(C13⋊C3) | ΓL(1,𝔽8) | semidirect |
| 19. C72×C13 | C3×A4 | semidirect |
| 22. C22×#3862 | C13⋊C3 | semidirect |
| 27. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 35. C22×C72 | C3×C13⋊C3 | semidirect |
| 40. C22⋊(C13⋊C3) | #3862 | direct (N × H) |
| 43. #3862 | C22⋊(C13⋊C3) | direct (N × H) |
| 47. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 55. C22×C13 | C3×#3862 | semidirect |
| 56. C72 | C3×C22⋊(C13⋊C3) | semidirect |
| 63. C22×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 72. C13 | A4×#3862 | semidirect |
| 78. C7 | ΓL(1,𝔽8)×C22⋊(C13⋊C3) | semidirect |
| 80. C22 | C13⋊C3×#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#3862 | 3 |
| C72×C22⋊(C13⋊C3) | 3 |
| C22⋊(C13⋊#3862) | 3 |
| C13⋊C3×#3862 | 4 |
| ΓL(1,𝔽8)×C22⋊(C13⋊C3) | 7 |
| A4×#3862 | 13 |