Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
572 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 144 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. C23×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 3. C2×(C22⋊Dic7)⋊C3 | C2 | semidirect |
| 4. C2×(C22⋊Dic7)⋊C3 | C2 | semidirect |
| 5. ΓL(1,𝔽8)⋊#95 | C2 | semidirect |
| 6. #89992 | C3 | semidirect |
| 11. C2×D4×ΓL(1,𝔽8) | C4 | semidirect |
| 20. C23×Dic7 | C2×C3 | semidirect |
| 21. C2×C22⋊Dic7 | C2×C3 | semidirect |
| 22. C2×C22⋊Dic7 | C2×C3 | semidirect |
| 23. C7⋊#95 | C2×C3 | semidirect |
| 32. C23×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 39. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 46. C2×ΓL(1,𝔽8)⋊C4 | D4 | semidirect |
| 51. C2×C7×D4 | C3×C4 | semidirect |
| 73. C22×ΓL(1,𝔽8) | C22⋊C4 | semidirect |
| 90. C23×C7 | C2×C3×C4 | semidirect |
| 97. C2×C4×C7 | C2×C3×C4 | semidirect |
| 104. C2×Dic7 | C3×D4 | semidirect |
| 138. C22×C7 | C3×C22⋊C4 | semidirect |
| 169. ΓL(1,𝔽8) | #386 | semidirect |
| 174. C2×D4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 214. C23 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 228. C2×C4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 229. C7 | C3×#386 | semidirect |
| 246. C22 | (C22⋊Dic7)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×ΓL(1,𝔽8) | 2 |
| C23×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×(C22⋊Dic7)⋊C3 | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| #89992 | 3 |
| C3×#386 | 7 |