Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C7×C3⋊C8 | C2 | semidirect |
| 3. C22×C3×C7⋊C8 | C2 | semidirect |
| 4. C2×#66559 | C2 | direct (N × H) |
| 11. C2×C7×C3⋊C8 | C22 | semidirect |
| 12. C2×C3×C7⋊C8 | C22 | semidirect |
| 13. #66559 | C22 | direct (N × H) |
| 16. C22×C7⋊C8 | D3 | semidirect |
| 27. C3×C7⋊C8 | C23 | semidirect |
| 28. C7×C3⋊C8 | C23 | semidirect |
| 35. C2×C7⋊C8 | C2×D3 | semidirect |
| 39. C22×C3⋊C8 | D7 | semidirect |
| 41. C22×C3×C7 | M16 | semidirect |
| 58. C7⋊C8 | C22×D3 | semidirect |
| 65. C2×C3⋊C8 | C2×D7 | semidirect |
| 67. C2×C3×C7 | C2×M16 | semidirect |
| 74. C22×C7 | ΓL(1,𝔽25) | semidirect |
| 90. C3⋊C8 | C22×D7 | semidirect |
| 91. C3×C7 | C22×M16 | semidirect |
| 100. C2×C7 | C2×ΓL(1,𝔽25) | semidirect |
| 103. C22×C3 | #1131 | semidirect |
| 120. C7 | C22×ΓL(1,𝔽25) | semidirect |
| 121. C2×C3 | C2×#1131 | semidirect |
| 126. C22 | #66559 | direct (N × H) |
| 131. C3 | C22×#1131 | semidirect |
| 133. C2 | C2×#66559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×#66559 | 2 |
| C22×#1131 | 3 |
| C22×ΓL(1,𝔽25) | 7 |