Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20295654 | C2 | semidirect |
| 3. #20295391 | C2 | semidirect |
| 4. #20295386 | C2 | semidirect |
| 5. #20295381 | C2 | semidirect |
| 6. #20295373 | C2 | semidirect |
| 7. #20295032 | C2 | semidirect |
| 8. #20295028 | C2 | semidirect |
| 9. #20295023 | C2 | semidirect |
| 10. C2×#16812621 | C2 | semidirect |
| 11. #405×C109 | C2 | semidirect |
| 14. #16812699 | C22 | semidirect |
| 17. #16812691 | C22 | semidirect |
| 26. #16812624 | C22 | semidirect |
| 27. #16812624 | C22 | semidirect |
| 28. #16812624 | C22 | semidirect |
| 33. #16812621 | C22 | semidirect |
| 34. #16812621 | C22 | semidirect |
| 35. #16812621 | C22 | semidirect |
| 39. #97×C109 | C22 | semidirect |
| 40. C4×C8×C109 | C22 | semidirect |
| 136. C109 | #3136 | semidirect |
| 147. #405 | D109 | semidirect |
| 175. #97 | C2×D109 | semidirect |
| 176. C4×C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295654 | 2 |
| #20295595 | 2 |
| #20295391 | 2 |
| #20295386 | 2 |
| #20295381 | 2 |
| #20295373 | 2 |
| #20295032 | 2 |
| #20295028 | 2 |
| #20295023 | 2 |
| C2×#16812621 | 2 |
| #405×C109 | 2 |
| #3136 | 109 |