Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
132 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 132 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⋊#3862 | C3 | semidirect |
| 2. C22⋊#14274263 | C3 | semidirect |
| 3. C7×C13×C22⋊ΓL(1,𝔽8) | C3 | semidirect |
| 4. C7×C22⋊#63270 | C3 | semidirect |
| 9. C22×C72×C13 | C32 | semidirect |
| 10. C13⋊#3862 | A4 | semidirect |
| 19. C22⋊#63270 | ΓL(1,𝔽8) | semidirect |
| 20. C13×C22⋊ΓL(1,𝔽8) | ΓL(1,𝔽8) | semidirect |
| 27. C72×C13 | C3×A4 | semidirect |
| 30. C7×C22⋊ΓL(1,𝔽8) | C13⋊C3 | semidirect |
| 37. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 38. C22×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 51. C22×C72 | C3×C13⋊C3 | semidirect |
| 66. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 67. C7×C13 | A4×ΓL(1,𝔽8) | semidirect |
| 72. C22⋊ΓL(1,𝔽8) | #63270 | semidirect |
| 80. C22×C13 | ΓL(1,𝔽8)2 | semidirect |
| 81. C72 | A4×C13⋊C3 | semidirect |
| 90. C22×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 91. C22×C7 | C3×#63270 | semidirect |
| 105. C13 | #3862⋊A4 | semidirect |
| 112. C7 | A4×#63270 | semidirect |
| 113. C7 | #63271⋊A4 | semidirect |
| 115. C22 | ΓL(1,𝔽8)×#63270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13⋊#3862 | 3 |
| C22⋊#14274263 | 3 |
| C7×C13×C22⋊ΓL(1,𝔽8) | 3 |
| C7×C22⋊#63270 | 3 |
| ΓL(1,𝔽8)×#63270 | 4 |
| #63271⋊A4 | 7 |
| A4×#63270 | 7 |
| #3862⋊A4 | 13 |