Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 40 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 | C2 | (C13⋊C3)⋊#64425 |
| commutator, hypocenter | C72×C13 | C32×C4 |
| Fitting, socle, cosocle | C2×C72×C13 | C2×C32 |
| prime radical | C2×C13⋊C3×#3862 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21439560 | C3 | semidirect |
| 3. #21439530 | C3 | semidirect |
| 4. #21439528 | C3 | semidirect |
| 5. C13⋊C3×#3862 | C4 | semidirect |
| 10. C7⋊Dic91 | C32 | semidirect |
| 11. C13⋊#3862 | C3×C4 | semidirect |
| 12. C13×#3862 | C3×C4 | semidirect |
| 13. C72×C13⋊C3 | C3×C4 | semidirect |
| 24. C72×C13 | C32×C4 | semidirect |
| 43. C7×C13⋊C3 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 55. #3862 | Dic13⋊C3 | semidirect |
| 60. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 71. C72 | C3×Dic13⋊C3 | semidirect |
| 79. C13⋊C3 | #10596875 | semidirect |
| 92. C13 | C3×#10596875 | semidirect |
| 98. C7 | ΓL(1,𝔽8)⋊(Dic13⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13⋊C3×#3862 | 2 |
| #21439560 | 3 |
| #21439530 | 3 |
| #21439528 | 3 |
| ΓL(1,𝔽8)⋊(Dic13⋊C3) | 7 |
| C3×#10596875 | 13 |