Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
440 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 63 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 | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊#16838473 | C2 | semidirect |
| 2. C3⋊#16838446 | C2 | semidirect |
| 3. C3×#16838448 | C2 | semidirect |
| 4. D39×C7⋊D7 | C3 | semidirect |
| 6. C3×#14274263 | C22 | semidirect |
| 7. C3⋊(C7⋊D91) | C2×C3 | semidirect |
| 8. C72×D39 | C2×C3 | semidirect |
| 9. C3×C13×C7⋊D7 | C2×C3 | semidirect |
| 12. #16838448 | D3 | semidirect |
| 16. C3×C72×C13 | C22×C3 | semidirect |
| 18. #14274263 | C2×D3 | semidirect |
| 24. C13×C7⋊D7 | C3×D3 | semidirect |
| 32. C72×C13 | C2×C3×D3 | semidirect |
| 36. C7×D39 | AGL(1,𝔽7) | semidirect |
| 47. C3×C7⋊D7 | D13⋊C3 | semidirect |
| 52. C3×C7×C13 | C2×AGL(1,𝔽7) | semidirect |
| 65. C3×C72 | C2×D13⋊C3 | semidirect |
| 74. C7⋊D7 | C3⋊(D13⋊C3) | semidirect |
| 75. C7×C13 | D3×AGL(1,𝔽7) | semidirect |
| 80. D39 | #64424 | semidirect |
| 87. C72 | C2×C3⋊(D13⋊C3) | semidirect |
| 95. C3×C13 | C2×#64424 | semidirect |
| 103. C3×C7 | #10587716⋊C2 | semidirect |
| 112. C13 | D3×#64424 | semidirect |
| 116. C7 | #10587720⋊D3 | semidirect |
| 127. C3 | #21439599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#16838473 | 2 |
| C3⋊#16838446 | 2 |
| C3×#16838448 | 2 |
| D39×C7⋊D7 | 3 |
| #21439599 | 3 |
| #10587720⋊D3 | 7 |
| D3×#64424 | 13 |