Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
270 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 52 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. #20296007 | C2 | semidirect |
| 2. #20295931 | C2 | semidirect |
| 3. #20295930 | C2 | semidirect |
| 7. #16812758 | C22 | semidirect |
| 9. C2×D4×D109 | C4 | semidirect |
| 12. #16812688 | C4 | semidirect |
| 15. #16812656 | C4 | semidirect |
| 16. #124×C109 | C4 | semidirect |
| 85. C109 | #2128 | semidirect |
| 95. #124 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296007 | 2 |
| #20295931 | 2 |
| #20295930 | 2 |
| #20295594 | 2 |
| #2128 | 109 |