Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20297302 | C2 | semidirect |
| 2. #20297299 | C2 | semidirect |
| 3. #20297297 | C2 | semidirect |
| 4. #20297293 | C2 | semidirect |
| 5. #20297290 | C2 | semidirect |
| 6. #20297290 | C2 | semidirect |
| 7. #20297289 | C2 | semidirect |
| 8. #20297287 | C2 | semidirect |
| 9. #20297282 | C2 | semidirect |
| 10. #20297282 | C2 | semidirect |
| 12. #20297269 | C2 | semidirect |
| 13. C4×C22⋊D223 | C2 | semidirect |
| 14. #20297262 | C2 | semidirect |
| 15. C22⋊Q8×C223 | C2 | semidirect |
| 103. C223 | #542 | semidirect |
| 115. C22⋊Q8 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297302 | 2 |
| #20297299 | 2 |
| #20297297 | 2 |
| #20297293 | 2 |
| #20297290 | 2 |
| #20297289 | 2 |
| #20297287 | 2 |
| #20297282 | 2 |
| #20297277 | 2 |
| #20297269 | 2 |
| C4×C22⋊D223 | 2 |
| #20297262 | 2 |
| C22⋊Q8×C223 | 2 |
| #542 | 223 |