Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 4. (ΓL(1,𝔽8)⋊C4)⋊C8 | C2 | semidirect |
| 5. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 6. #89609 | C3 | semidirect |
| 19. C7×C4⋊C8 | C2×C3 | semidirect |
| 20. Dic7⋊C8 | C2×C3 | semidirect |
| 21. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 56. C4×ΓL(1,𝔽8) | M16 | semidirect |
| 61. ΓL(1,𝔽8)⋊C4 | M16 | semidirect |
| 94. C4⋊C8 | AGL(1,𝔽7) | semidirect |
| 100. C4×C7 | C3×M16 | semidirect |
| 105. Dic7 | C3×M16 | semidirect |
| 119. ΓL(1,𝔽8) | #423 | semidirect |
| 158. C7 | C3×#423 | semidirect |
| 171. C4 | #1131⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1131⋊C3 | 2 |
| C42×AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89609 | 3 |
| C3×#423 | 7 |