Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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×#1144 | C2 | semidirect |
| 5. C3×C7×#101 | C2 | semidirect |
| 6. C3×#6398 | C2 | semidirect |
| 7. C3×#6396 | C2 | semidirect |
| 8. #89527 | C3 | direct (N × H) |
| 24. C2×#1144 | C2×C3 | semidirect |
| 28. C7×#101 | C2×C3 | semidirect |
| 29. #6398 | C2×C3 | semidirect |
| 30. #6396 | C2×C3 | semidirect |
| 69. C3×#101 | D7 | semidirect |
| 118. #101 | C3×D7 | semidirect |
| 142. C3×C7 | #473 | semidirect |
| 184. C7 | C3×#473 | semidirect |
| 195. C3 | #89527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1144 | 2 |
| C3×#6505 | 2 |
| C3×#6472 | 2 |
| C3×#6470 | 2 |
| C3×C7×#101 | 2 |
| C3×#6398 | 2 |
| C3×#6396 | 2 |
| #89527 | 3 |
| C3×#473 | 7 |