Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
168 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21439603 |
| commutator, hypocenter | C72×C13 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C3×C4 |
| prime radical | C3×D13⋊#3862 | C2 |
| cosocle | C72×D13 | C2×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C7⋊(C7⋊#261) | C3 | semidirect |
| 3. #21439603 | C3 | direct (N × H) |
| 4. C3×C13⋊#3862 | C4 | semidirect |
| 9. C7⋊(C7⋊#261) | C32 | semidirect |
| 10. C3×C72×C13 | C3×C4 | semidirect |
| 11. C13⋊#3862 | C3×C4 | semidirect |
| 24. C72×C13 | C32×C4 | semidirect |
| 40. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 41. C3×C7×C13 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 53. C3×C72 | AGL(1,𝔽13) | semidirect |
| 60. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 61. C7×C13 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 72. C72 | C3×AGL(1,𝔽13) | semidirect |
| 78. C3×C13 | #10596875 | semidirect |
| 86. C3×C7 | #11763984 | semidirect |
| 87. C3×C7 | #11763985 | semidirect |
| 94. C13 | C3×#10596875 | semidirect |
| 99. C7 | C3×#11763985 | semidirect |
| 100. C7 | C3×#11763984 | semidirect |
| 105. C3 | #21439603 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D13⋊#3862 | 2 |
| C3×C7⋊(C7⋊#261) | 3 |
| #21439603 | 3 |
| C3×#11763984 | 7 |
| C3×#11763985 | 7 |
| C3×#10596875 | 13 |