Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295834 | C2 | semidirect |
| 2. #20295828 | C2 | semidirect |
| 3. #20295411 | C2 | semidirect |
| 4. #20295298 | C2 | semidirect |
| 5. #20295296 | C2 | semidirect |
| 6. #20295291 | C2 | semidirect |
| 7. #20295202 | C2 | semidirect |
| 8. #20295199 | C2 | semidirect |
| 9. #20295143 | C2 | semidirect |
| 10. #20295141 | C2 | semidirect |
| 11. #578×C109 | C2 | semidirect |
| 18. #16812724 | C22 | semidirect |
| 23. C2×#13182016 | C22 | semidirect |
| 26. #16812706 | C22 | semidirect |
| 28. #16812688 | C22 | semidirect |
| 29. #16812635 | C22 | semidirect |
| 30. #16812634 | C22 | semidirect |
| 31. #16812626 | C22 | semidirect |
| 32. #16812626 | C22 | semidirect |
| 34. #16812618 | C22 | semidirect |
| 35. #16812615 | C22 | semidirect |
| 36. C8×Dic109 | C22 | semidirect |
| 37. 2−1+4×C109 | C22 | semidirect |
| 39. #137×C109 | C22 | semidirect |
| 43. C2×Q16×C109 | C22 | semidirect |
| 44. #131×C109 | C22 | semidirect |
| 150. C109 | #3290 | semidirect |
| 151. #578 | D109 | semidirect |
| 162. 2−1+4 | C2×D109 | semidirect |
| 167. #137 | C2×D109 | semidirect |
| 178. C2×Q16 | C2×D109 | semidirect |
| 185. #131 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295834 | 2 |
| #20295828 | 2 |
| #20295411 | 2 |
| #20295298 | 2 |
| #20295296 | 2 |
| #20295291 | 2 |
| #20295202 | 2 |
| #20295199 | 2 |
| #20295143 | 2 |
| #20295141 | 2 |
| #578×C109 | 2 |
| #3290 | 109 |