Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20295583 | C2 | semidirect |
| 3. #20295362 | C2 | semidirect |
| 4. #20295307 | C2 | semidirect |
| 5. #20295232 | C2 | semidirect |
| 7. #20295128 | C2 | semidirect |
| 8. #432×C109 | C2 | semidirect |
| 12. #16812699 | C22 | semidirect |
| 13. #16812699 | C22 | semidirect |
| 18. C4×Dic218 | C22 | semidirect |
| 26. #16812633 | C22 | semidirect |
| 27. #16812624 | C22 | semidirect |
| 30. C4⋊C8×C109 | C22 | semidirect |
| 32. #97×C109 | C22 | semidirect |
| 113. C109 | #3110 | semidirect |
| 121. #432 | D109 | semidirect |
| 141. C4⋊C8 | C2×D109 | semidirect |
| 145. #97 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295583 | 2 |
| C2×C4×D436 | 2 |
| #20295362 | 2 |
| #20295307 | 2 |
| #20295232 | 2 |
| #20295179 | 2 |
| #20295128 | 2 |
| #432×C109 | 2 |
| #3110 | 109 |