Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C13×C49 | C22×C3 |
| Frattini | C7 | D3×ΓL(1,𝔽8)⋊D13 |
| socle | C3×C7×C13 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊((C49⋊C3)⋊D13) | C2 | semidirect |
| 2. D3×C13×C49⋊C3 | C2 | semidirect |
| 3. C3×(C49⋊C3)⋊D13 | C2 | semidirect |
| 4. D3×D637 | C3 | semidirect |
| 6. C3×C13×C49⋊C3 | C22 | semidirect |
| 7. D1911 | C2×C3 | semidirect |
| 8. D3×C13×C49 | C2×C3 | semidirect |
| 9. C3×D637 | C2×C3 | semidirect |
| 13. (C49⋊C3)⋊D13 | D3 | direct (N × H) |
| 16. C3×C13×C49 | C22×C3 | semidirect |
| 18. C13×C49⋊C3 | C2×D3 | semidirect |
| 25. D637 | C3×D3 | semidirect |
| 29. D3×C49⋊C3 | D13 | semidirect |
| 32. C13×C49 | C2×C3×D3 | semidirect |
| 43. C3×C49⋊C3 | C2×D13 | semidirect |
| 47. D3×C49 | C3×D13 | semidirect |
| 65. C3×C49 | C2×C3×D13 | semidirect |
| 67. C49⋊C3 | D3×D13 | semidirect |
| 84. D3×C13 | D49⋊C3 | semidirect |
| 87. C49 | C3×D3×D13 | semidirect |
| 97. C3×C13 | C2×D49⋊C3 | semidirect |
| 112. C13 | D3×D49⋊C3 | semidirect |
| 123. D3 | (C49⋊C3)⋊D13 | direct (N × H) |
| 127. C3 | C2×(C49⋊C3)⋊D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊((C49⋊C3)⋊D13) | 2 |
| D3×C13×C49⋊C3 | 2 |
| C3×(C49⋊C3)⋊D13 | 2 |
| D3×D637 | 3 |
| C2×(C49⋊C3)⋊D13 | 3 |
| D3×ΓL(1,𝔽8)⋊D13 | 7 |
| D3×D49⋊C3 | 13 |