Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
152 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 37 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, hypocenter | C72×C13 | C32×C4 |
| prime radical | D13⋊C3×#3862 | C2 |
| cosocle | C72×D13 | C2×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21439633 | C3 | semidirect |
| 3. #21439630 | C3 | semidirect |
| 4. #21439629 | C3 | semidirect |
| 5. C7×#11763979 | C3 | semidirect |
| 6. C13⋊C3×#3862 | C4 | semidirect |
| 13. C7×C7⋊#261 | C32 | semidirect |
| 14. C13⋊#3862 | C3×C4 | semidirect |
| 15. C13⋊#3862 | C3×C4 | semidirect |
| 16. C13×#3862 | C3×C4 | semidirect |
| 17. C72×C13⋊C3 | C3×C4 | semidirect |
| 28. #11763979 | ΓL(1,𝔽8) | semidirect |
| 33. C72×C13 | C32×C4 | semidirect |
| 49. C7⋊#261 | C3×ΓL(1,𝔽8) | semidirect |
| 60. C7×C13⋊C3 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 61. C7×C13⋊C3 | C4×ΓL(1,𝔽8) | semidirect |
| 78. #3862 | AGL(1,𝔽13) | semidirect |
| 84. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 85. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 101. C72 | C3×AGL(1,𝔽13) | semidirect |
| 114. C13⋊C3 | #10596872 | semidirect |
| 132. C13 | C3×#10596872 | semidirect |
| 139. C7 | ΓL(1,𝔽8)⋊AGL(1,𝔽13) | semidirect |
| 140. C7 | ΓL(1,𝔽8)×AGL(1,𝔽13) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13⋊C3×#3862 | 2 |
| #21439633 | 3 |
| #21439630 | 3 |
| #21439629 | 3 |
| C7×#11763979 | 3 |
| ΓL(1,𝔽8)×AGL(1,𝔽13) | 7 |
| ΓL(1,𝔽8)⋊AGL(1,𝔽13) | 7 |
| C3×#10596872 | 13 |