Finite Group DatabasebetaFinite Group Databasebeta← C2×D4×C22⋊ΓL(1,𝔽8) #13062310
Order 1344.
634 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C23×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 2. D4×C22⋊ΓL(1,𝔽8) | C2 | direct (N × H) |
| 3. C2×C4×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 4. C23×C7×D4 | C3 | semidirect |
| 7. C22×C22⋊ΓL(1,𝔽8) | C22 | semidirect |
| 8. C4×C22⋊ΓL(1,𝔽8) | C22 | semidirect |
| 10. C25×C7 | C2×C3 | semidirect |
| 15. C22×C7×D4 | C2×C3 | semidirect |
| 16. C23×C4×C7 | C2×C3 | semidirect |
| 19. C2×C22⋊ΓL(1,𝔽8) | D4 | direct (N × H) |
| 30. C24×C7 | C22×C3 | semidirect |
| 40. C2×C7×D4 | A4 | semidirect |
| 44. C22×C4×C7 | C22×C3 | semidirect |
| 48. C22⋊ΓL(1,𝔽8) | C2×D4 | direct (N × H) |
| 53. C23×D4 | ΓL(1,𝔽8) | semidirect |
| 70. C23×C7 | C3×D4 | semidirect |
| 71. C23×C7 | C2×A4 | semidirect |
| 76. C7×D4 | C2×A4 | semidirect |
| 82. C2×C4×C7 | C2×A4 | semidirect |
| 91. C25 | C2×ΓL(1,𝔽8) | semidirect |
| 96. C22×D4 | C2×ΓL(1,𝔽8) | semidirect |
| 97. C23×C4 | C2×ΓL(1,𝔽8) | semidirect |
| 114. C22×C7 | C2×C3×D4 | semidirect |
| 116. C22×C7 | C22×A4 | semidirect |
| 118. C4×C7 | C22×A4 | semidirect |
| 132. C24 | C22×ΓL(1,𝔽8) | semidirect |
| 142. C2×D4 | C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 146. C22×C4 | C22×ΓL(1,𝔽8) | semidirect |
| 152. C2×C7 | D4×A4 | semidirect |
| 175. C23 | D4×ΓL(1,𝔽8) | semidirect |
| 177. C23 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 181. D4 | C2×C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 187. C2×C4 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 188. C7 | C2×D4×A4 | semidirect |
| 208. C22 | C2×D4×ΓL(1,𝔽8) | semidirect |
| 210. C22 | C22×C22⋊ΓL(1,𝔽8) | semidirect |
| 212. C4 | C22×C22⋊ΓL(1,𝔽8) | semidirect |
| 219. C2 | D4×C22⋊ΓL(1,𝔽8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊ΓL(1,𝔽8) | 2 |
| D4×C22⋊ΓL(1,𝔽8) | 2 |
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C23×C7×D4 | 3 |
| C2×D4×ΓL(1,𝔽8) | 4 |
| C2×D4×A4 | 7 |