Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 3. C2×#1136⋊C3 | C2 | semidirect |
| 4. #6409⋊C3 | C2 | semidirect |
| 5. #6406⋊C3 | C2 | semidirect |
| 6. #90004 | C3 | semidirect |
| 8. #41×ΓL(1,𝔽8) | C4 | semidirect |
| 20. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 21. C2×#1136 | C2×C3 | semidirect |
| 22. #6409 | C2×C3 | semidirect |
| 23. #6406 | C2×C3 | semidirect |
| 28. Q8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 31. D4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 42. C7×#41 | C3×C4 | semidirect |
| 74. C7×Q8 | C2×C3×C4 | semidirect |
| 77. C7×D4 | C2×C3×C4 | semidirect |
| 137. ΓL(1,𝔽8) | #417 | semidirect |
| 139. #41 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 170. Q8 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 173. D4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 183. C7 | C3×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×ΓL(1,𝔽8) | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C2×#1136⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6406⋊C3 | 2 |
| #90004 | 3 |
| C3×#417 | 7 |