Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20297349 | C2 | semidirect |
| 2. #20297330 | C2 | semidirect |
| 3. #20297328 | C2 | semidirect |
| 4. #20297326 | C2 | semidirect |
| 5. #20297323 | C2 | semidirect |
| 6. D8×D223 | C2 | semidirect |
| 7. #20297310 | C2 | semidirect |
| 8. C2×D8×C223 | C2 | semidirect |
| 10. #16813170 | C22 | semidirect |
| 12. #16813169 | C22 | semidirect |
| 15. D4×D223 | C22 | semidirect |
| 16. Dic892 | C22 | semidirect |
| 17. #16813159 | C22 | semidirect |
| 18. #16813158 | C22 | semidirect |
| 19. D1784 | C22 | semidirect |
| 20. #16813155 | C22 | semidirect |
| 21. #16813154 | C22 | semidirect |
| 22. #16813153 | C22 | semidirect |
| 23. C8×D223 | C22 | semidirect |
| 24. C2×D4×C223 | C22 | semidirect |
| 25. D8×C223 | C22 | semidirect |
| 26. D8×C223 | C22 | semidirect |
| 27. C2×C8×C223 | C22 | semidirect |
| 62. C223 | #576 | semidirect |
| 70. C2×D8 | D223 | semidirect |
| 79. C2×D4 | C2×D223 | semidirect |
| 85. D8 | C2×D223 | semidirect |
| 86. D8 | C2×D223 | semidirect |
| 90. C2×C8 | C2×D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297349 | 2 |
| #20297330 | 2 |
| #20297328 | 2 |
| #20297326 | 2 |
| #20297323 | 2 |
| D8×D223 | 2 |
| #20297310 | 2 |
| C2×D8×C223 | 2 |
| #576 | 223 |