Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20296036 | C2 | semidirect |
| 3. #20295894 | C2 | semidirect |
| 13. C2×#13182012 | C4 | semidirect |
| 15. C22×#11724784 | C4 | semidirect |
| 16. C2×C8×D109 | C4 | semidirect |
| 18. C2×M16×C109 | C4 | semidirect |
| 86. C109 | #1812 | semidirect |
| 96. C2×M16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296036 | 2 |
| #20296005 | 2 |
| #20295894 | 2 |
| C2×#16812707 | 2 |
| #1812 | 109 |