Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #20295975 | C2 | semidirect |
| 3. C4×C4⋊#89137 | C2 | semidirect |
| 5. #20295962 | C2 | semidirect |
| 6. C42×#89137 | C2 | semidirect |
| 17. #16812658 | C4 | semidirect |
| 18. #16812657 | C4 | semidirect |
| 19. #16812656 | C4 | semidirect |
| 20. #16812656 | C4 | semidirect |
| 21. #16812655 | C4 | semidirect |
| 26. #117×C109 | C4 | semidirect |
| 109. C109 | #2298 | semidirect |
| 123. #117 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295976 | 2 |
| #20295975 | 2 |
| C4×C4⋊#89137 | 2 |
| C4×C22⋊#89137 | 2 |
| #20295962 | 2 |
| C42×#89137 | 2 |
| #117×D109 | 2 |
| #2298 | 109 |