Finite Group DatabasebetaFinite Group Databasebeta← C2×(C22⋊(C7⋊C8))⋊C3 #13052106
Order 1344.
404 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 160 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×ΓL(1,𝔽8)⋊C8 | C2 | semidirect |
| 3. (C22⋊(C7⋊C8))⋊C3 | C2 | direct (N × H) |
| 4. C2×C22⋊(C7⋊C8) | C3 | semidirect |
| 12. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 14. C22×C7⋊C8 | C2×C3 | semidirect |
| 15. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 19. C23×ΓL(1,𝔽8) | C8 | semidirect |
| 37. C2×C7⋊C8 | C22×C3 | semidirect |
| 46. C22×ΓL(1,𝔽8) | C2×C8 | semidirect |
| 55. C23×C7 | C3×C8 | semidirect |
| 75. C2×ΓL(1,𝔽8) | C22⋊C8 | semidirect |
| 87. C22×C7 | C2×C3×C8 | semidirect |
| 106. ΓL(1,𝔽8) | C2×C22⋊C8 | semidirect |
| 116. C2×C7 | C3×C22⋊C8 | semidirect |
| 133. C23 | ΓL(1,𝔽8)⋊C8 | semidirect |
| 144. C7 | C2×C3×C22⋊C8 | semidirect |
| 154. C22 | C2×ΓL(1,𝔽8)⋊C8 | semidirect |
| 163. C2 | (C22⋊(C7⋊C8))⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| C2×C22⋊(C7⋊C8) | 3 |
| C2×C3×C22⋊C8 | 7 |