Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#1136⋊C3 | C2 | semidirect |
| 3. C22×ΓL(1,𝔽8)⋊C8 | C2 | semidirect |
| 4. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 5. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 6. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 7. #6377⋊C3 | C2 | semidirect |
| 8. #89783 | C3 | semidirect |
| 23. C2×#1136 | C2×C3 | semidirect |
| 24. C22×C7⋊C8 | C2×C3 | semidirect |
| 25. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 26. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 27. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 28. #6377 | C2×C3 | semidirect |
| 45. ΓL(1,𝔽8)⋊C8 | D4 | semidirect |
| 71. C22×ΓL(1,𝔽8) | M16 | semidirect |
| 95. C7⋊C8 | C3×D4 | semidirect |
| 126. C22×C7 | C3×M16 | semidirect |
| 150. ΓL(1,𝔽8) | #435 | semidirect |
| 198. C7 | C3×#435 | semidirect |
| 209. C22 | #1136⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×ΓL(1,𝔽8) | 2 |
| C2×#1136⋊C3 | 2 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #6377⋊C3 | 2 |
| #89783 | 3 |
| C3×#435 | 7 |