Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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. D4×Dic223 | C2 | semidirect |
| 3. #20297266 | C2 | semidirect |
| 4. #20297235 | C2 | semidirect |
| 5. #20297226 | C2 | semidirect |
| 6. #20297214 | C2 | semidirect |
| 7. #102×C223 | C2 | semidirect |
| 11. #16813155 | C4 | semidirect |
| 22. D892 | C2×C4 | semidirect |
| 28. C223⋊C8 | C2×C4 | semidirect |
| 31. D4×C223 | C2×C4 | semidirect |
| 53. C223 | #442 | semidirect |
| 60. #102 | D223 | semidirect |
| 79. D4 | C4×D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813155 | 2 |
| D4×Dic223 | 2 |
| #20297266 | 2 |
| #20297235 | 2 |
| #20297226 | 2 |
| #20297214 | 2 |
| #102×C223 | 2 |
| #442 | 223 |