Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19153211 |
| commutator, hypocenter | C72×C13 | C32×C4 |
| Frattini | C2 | C2×#19153211 |
| Fitting | C4×C72×C13 | C32 |
| socle, cosocle | C2×C72×C13 | C2×C32 |
| prime radical | C2×#19153211 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C13×#3862 | C3 | semidirect |
| 3. C4×#14274262 | C3 | semidirect |
| 4. C4×C7×#63270 | C3 | semidirect |
| 5. #19153211 | C4 | direct (N × H) |
| 10. C4×C72×C13 | C32 | semidirect |
| 11. C13×#3862 | C3×C4 | semidirect |
| 12. #14274262 | C3×C4 | semidirect |
| 13. C7×#63270 | C3×C4 | semidirect |
| 19. C4×#63270 | ΓL(1,𝔽8) | semidirect |
| 24. C72×C13 | C32×C4 | semidirect |
| 25. C4×#3862 | C13⋊C3 | semidirect |
| 36. C4×C7×C13 | C3×ΓL(1,𝔽8) | semidirect |
| 42. #63270 | C4×ΓL(1,𝔽8) | semidirect |
| 47. C4×C72 | C3×C13⋊C3 | semidirect |
| 53. #3862 | C4×C13⋊C3 | semidirect |
| 60. C7×C13 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 70. C4×C13 | ΓL(1,𝔽8)2 | semidirect |
| 71. C72 | C3×C4×C13⋊C3 | semidirect |
| 82. C4×C7 | ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 92. C13 | C4×ΓL(1,𝔽8)2 | semidirect |
| 98. C7 | C4×ΓL(1,𝔽8)×C13⋊C3 | semidirect |
| 102. C4 | #19153211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153211 | 2 |
| C4×C13×#3862 | 3 |
| C4×#14274262 | 3 |
| C4×C7×#63270 | 3 |
| C4×ΓL(1,𝔽8)×C13⋊C3 | 7 |
| C4×ΓL(1,𝔽8)2 | 13 |