Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
132 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 132 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, hypercenter | C2 | C3⋊#16838413 |
| commutator, cosocle, hypocenter | C3×C13×C49 | C22×C3 |
| Frattini | C7 | C2×C3⋊#10587716 |
| Fitting | C2×C3×C13×C49 | C2×C3 |
| socle | C2×C3×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#14274254 | C2 | semidirect |
| 2. C3⋊#16838413 | C2 | direct (N × H) |
| 3. C2×C49×D39 | C3 | semidirect |
| 5. C3×#14274254 | C22 | semidirect |
| 6. C49×D39 | C2×C3 | semidirect |
| 8. C2×#14274254 | D3 | semidirect |
| 10. C2×C3×C13×C49 | C2×C3 | semidirect |
| 13. C3×C13×C49 | C22×C3 | semidirect |
| 15. #14274254 | C2×D3 | semidirect |
| 19. C2×C13×C49 | C3×D3 | semidirect |
| 26. C13×C49 | C2×C3×D3 | semidirect |
| 37. C2×C3×C49 | D13⋊C3 | semidirect |
| 51. C2×D39 | C49⋊C3 | semidirect |
| 53. C3×C49 | C2×D13⋊C3 | semidirect |
| 60. C2×C49 | C3⋊(D13⋊C3) | semidirect |
| 64. C2×C3×C13 | C2×C49⋊C3 | semidirect |
| 65. D39 | C2×C49⋊C3 | semidirect |
| 71. C49 | C2×C3⋊(D13⋊C3) | semidirect |
| 77. C3×C13 | C22×C49⋊C3 | semidirect |
| 82. C2×C13 | D3×C49⋊C3 | semidirect |
| 91. C13 | C2×D3×C49⋊C3 | semidirect |
| 99. C2×C3 | #16838413 | semidirect |
| 104. C3 | C2×#16838413 | semidirect |
| 106. C2 | C3⋊#16838413 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#14274254 | 2 |
| C3⋊#16838413 | 2 |
| C2×C49×D39 | 3 |
| C2×#16838413 | 3 |
| C2×C3⋊#10587716 | 7 |
| C2×D3×C49⋊C3 | 13 |