Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 110 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×C3×#1132 | C2 | semidirect |
| 3. C3×#6432 | C2 | semidirect |
| 4. C3×C4×C7×C8 | C2 | semidirect |
| 5. #89465 | C3 | direct (N × H) |
| 13. C2×#1132 | C2×C3 | semidirect |
| 15. #6432 | C2×C3 | semidirect |
| 16. C4×C7×C8 | C2×C3 | semidirect |
| 25. C3×C7×C8 | D4 | semidirect |
| 36. C3×C4×C8 | D7 | semidirect |
| 40. C3×C4×C7 | SD16 | semidirect |
| 51. C7×C8 | C3×D4 | semidirect |
| 65. C4×C8 | C3×D7 | semidirect |
| 69. C4×C7 | C3×SD16 | semidirect |
| 79. C3×C8 | D28 | semidirect |
| 80. C3×C7 | #492 | semidirect |
| 95. C3×C4 | #1132 | semidirect |
| 104. C8 | C3×D28 | semidirect |
| 105. C7 | C3×#492 | semidirect |
| 113. C4 | C3×#1132 | semidirect |
| 115. C3 | #89465 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1132 | 2 |
| C3×#6437 | 2 |
| C3×#6432 | 2 |
| C3×C4×C7×C8 | 2 |
| #89465 | 3 |
| C3×#492 | 7 |