Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 80 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. C2×SD16×ΓL(1,𝔽8) | C2 | semidirect |
| 2. #6507⋊C3 | C2 | semidirect |
| 3. C2×#1143⋊C3 | C2 | semidirect |
| 5. C2×#1142⋊C3 | C2 | semidirect |
| 6. C2×#1132⋊C3 | C2 | semidirect |
| 7. C8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 8. #89947 | C3 | semidirect |
| 22. C2×C7×SD16 | C2×C3 | semidirect |
| 23. #6507 | C2×C3 | semidirect |
| 24. C2×#1143 | C2×C3 | semidirect |
| 26. C2×#1142 | C2×C3 | semidirect |
| 27. C2×#1132 | C2×C3 | semidirect |
| 28. C8×Dic7 | C2×C3 | semidirect |
| 45. C8×ΓL(1,𝔽8) | D4 | semidirect |
| 46. ΓL(1,𝔽8)⋊C8 | D4 | semidirect |
| 76. ΓL(1,𝔽8)⋊C4 | SD16 | semidirect |
| 93. C7×C8 | C3×D4 | semidirect |
| 94. C7⋊C8 | C3×D4 | semidirect |
| 115. C2×SD16 | AGL(1,𝔽7) | semidirect |
| 128. Dic7 | C3×SD16 | semidirect |
| 146. ΓL(1,𝔽8) | #492 | semidirect |
| 190. C8 | (C22⋊D7)⋊C3 | semidirect |
| 191. C7 | C3×#492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×ΓL(1,𝔽8) | 2 |
| #6507⋊C3 | 2 |
| C2×#1143⋊C3 | 2 |
| #6503⋊C3 | 2 |
| C2×#1142⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| #89947 | 3 |
| C3×#492 | 7 |