Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×D223 | C2 | semidirect |
| 3. C2×(C2×D223)⋊C4 | C2 | semidirect |
| 4. C2×(C2×D223)⋊C4 | C2 | semidirect |
| 5. C2×(C2×D223)⋊C4 | C2 | semidirect |
| 6. C223⋊#95 | C2 | semidirect |
| 7. #95×C223 | C2 | semidirect |
| 12. C2×D892 | C4 | semidirect |
| 35. C22×D223 | C2×C4 | semidirect |
| 44. C2×Dic223 | D4 | semidirect |
| 54. C2×C4×C223 | C2×C4 | semidirect |
| 55. C2×C4×C223 | D4 | semidirect |
| 76. C2×D223 | C22⋊C4 | semidirect |
| 91. C223 | #386 | semidirect |
| 99. #95 | D223 | semidirect |
| 146. C2×C4 | C4×D223 | semidirect |
| 147. C2×C4 | D892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D892 | 2 |
| C22×C4×D223 | 2 |
| C2×(C2×D223)⋊C4 | 2 |
| C223⋊#95 | 2 |
| #95×C223 | 2 |
| #386 | 223 |