Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20297299 | C2 | semidirect |
| 2. #20297295 | C2 | semidirect |
| 3. #20297293 | C2 | semidirect |
| 4. #20297288 | C2 | semidirect |
| 6. Q8×Dic223 | C2 | semidirect |
| 7. #20297266 | C2 | semidirect |
| 8. (C22⋊D223)⋊C4 | C2 | semidirect |
| 9. #20297262 | C2 | semidirect |
| 10. C2×C4×Dic223 | C2 | semidirect |
| 11. C22⋊Q8×C223 | C2 | semidirect |
| 74. C223 | #529 | semidirect |
| 80. C22⋊Q8 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297299 | 2 |
| #20297295 | 2 |
| #20297293 | 2 |
| #20297288 | 2 |
| #20297278 | 2 |
| Q8×Dic223 | 2 |
| #20297266 | 2 |
| (C22⋊D223)⋊C4 | 2 |
| #20297262 | 2 |
| C2×C4×Dic223 | 2 |
| C22⋊Q8×C223 | 2 |
| #529 | 223 |