Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 192 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×#1157⋊C3 | C2 | semidirect |
| 2. C22×C8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×Dic28⋊C3 | C2 | semidirect |
| 4. #6467⋊C3 | C2 | direct (N × H) |
| 5. C2×D56⋊C3 | C2 | semidirect |
| 6. C2×#1132⋊C3 | C2 | semidirect |
| 7. C2×#6467 | C3 | semidirect |
| 11. #1157⋊C3 | C22 | semidirect |
| 17. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 18. Dic28⋊C3 | C22 | semidirect |
| 19. D56⋊C3 | C22 | semidirect |
| 20. #1132⋊C3 | C22 | semidirect |
| 21. C2×#1157 | C2×C3 | semidirect |
| 22. C22×C7×C8 | C2×C3 | semidirect |
| 23. C2×Dic28 | C2×C3 | semidirect |
| 24. #6467 | C2×C3 | semidirect |
| 25. C2×D56 | C2×C3 | semidirect |
| 26. C2×#1132 | C2×C3 | semidirect |
| 46. #1157 | C22×C3 | semidirect |
| 52. C2×C7×C8 | C22×C3 | semidirect |
| 53. Dic28 | C22×C3 | semidirect |
| 54. D56 | C22×C3 | semidirect |
| 55. #1132 | C22×C3 | semidirect |
| 101. C2×ΓL(1,𝔽8) | #135 | semidirect |
| 109. C22×C8 | AGL(1,𝔽7) | semidirect |
| 134. ΓL(1,𝔽8) | C2×#135 | semidirect |
| 147. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 149. C2×C7 | C3×#135 | semidirect |
| 176. C7 | C2×C3×#135 | semidirect |
| 193. C2 | #6467⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C22×C8×ΓL(1,𝔽8) | 2 |
| C2×Dic28⋊C3 | 2 |
| #6467⋊C3 | 2 |
| C2×D56⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| C2×#6467 | 3 |
| C2×C3×#135 | 7 |