Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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. #41×D223 | C2 | semidirect |
| 2. #20297336 | C2 | semidirect |
| 3. #20297333 | C2 | semidirect |
| 4. #20297331 | C2 | semidirect |
| 5. #20297328 | C2 | semidirect |
| 6. #20297326 | C2 | semidirect |
| 7. #20297324 | C2 | semidirect |
| 8. C2×#16813153 | C2 | semidirect |
| 9. #135×C223 | C2 | semidirect |
| 12. #16813170 | C22 | semidirect |
| 15. Q8×D223 | C22 | semidirect |
| 17. D4×D223 | C22 | semidirect |
| 20. Dic892 | C22 | semidirect |
| 21. #16813160 | C22 | semidirect |
| 22. #16813159 | C22 | semidirect |
| 23. #16813158 | C22 | semidirect |
| 24. #16813157 | C22 | semidirect |
| 25. D1784 | C22 | semidirect |
| 26. #16813155 | C22 | semidirect |
| 27. #16813153 | C22 | semidirect |
| 28. #16813153 | C22 | semidirect |
| 29. C2×C223⋊C8 | C22 | semidirect |
| 30. #41×C223 | C22 | semidirect |
| 31. Q16×C223 | C22 | semidirect |
| 32. SD16×C223 | C22 | semidirect |
| 33. D8×C223 | C22 | semidirect |
| 34. C2×C8×C223 | C22 | semidirect |
| 75. C223 | #575 | semidirect |
| 84. #135 | D223 | semidirect |
| 91. #41 | C2×D223 | semidirect |
| 99. Q16 | C2×D223 | semidirect |
| 103. SD16 | C2×D223 | semidirect |
| 106. D8 | C2×D223 | semidirect |
| 110. C2×C8 | C2×D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D223 | 2 |
| #20297336 | 2 |
| #20297333 | 2 |
| #20297331 | 2 |
| #20297328 | 2 |
| #20297326 | 2 |
| #20297324 | 2 |
| C2×#16813153 | 2 |
| #135×C223 | 2 |
| #575 | 223 |