Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×#6453 | C2 | semidirect |
| 3. C3×C7×#103 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 6. C3×C8×Dic7 | C2 | semidirect |
| 8. #89572 | C3 | direct (N × H) |
| 21. #6453 | C2×C3 | semidirect |
| 22. C7×#103 | C2×C3 | semidirect |
| 23. #6409 | C2×C3 | semidirect |
| 25. C8×Dic7 | C2×C3 | semidirect |
| 55. C3×#103 | D7 | semidirect |
| 102. #103 | C3×D7 | semidirect |
| 130. C3×C7 | #488 | semidirect |
| 170. C7 | C3×#488 | semidirect |
| 186. C3 | #89572 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6510 | 2 |
| C3×#6453 | 2 |
| C3×C7×#103 | 2 |
| C3×#6409 | 2 |
| C3×#6395 | 2 |
| C3×C8×Dic7 | 2 |
| C3×#6383 | 2 |
| #89572 | 3 |
| C3×#488 | 7 |