Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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×Q8×AGL(1,𝔽7) | C2 | semidirect |
| 2. C2×SD16×ΓL(1,𝔽8) | C2 | semidirect |
| 4. C2×#1142⋊C3 | C2 | semidirect |
| 5. #6409⋊C3 | C2 | semidirect |
| 6. (C2×AGL(1,𝔽7))⋊C8 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89942 | C3 | semidirect |
| 24. C2×Q8×D7 | C2×C3 | semidirect |
| 25. C2×C7×SD16 | C2×C3 | semidirect |
| 27. C2×#1142 | C2×C3 | semidirect |
| 28. #6409 | C2×C3 | semidirect |
| 29. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 30. #6390 | C2×C3 | semidirect |
| 35. Q8×ΓL(1,𝔽8) | D4 | semidirect |
| 49. ΓL(1,𝔽8)⋊Q8 | D4 | semidirect |
| 80. C2×AGL(1,𝔽7) | SD16 | semidirect |
| 91. C7×Q8 | C3×D4 | semidirect |
| 105. Dic14 | C3×D4 | semidirect |
| 130. C2×SD16 | AGL(1,𝔽7) | semidirect |
| 141. C2×D7 | C3×SD16 | semidirect |
| 168. ΓL(1,𝔽8) | #448 | semidirect |
| 208. Q8 | (C22⋊D7)⋊C3 | semidirect |
| 222. C7 | C3×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽7) | 2 |
| C2×SD16×ΓL(1,𝔽8) | 2 |
| #6501⋊C3 | 2 |
| C2×#1142⋊C3 | 2 |
| #6409⋊C3 | 2 |
| (C2×AGL(1,𝔽7))⋊C8 | 2 |
| #6390⋊C3 | 2 |
| #89942 | 3 |
| C3×#448 | 7 |