Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #20295989 | C2 | semidirect |
| 4. #20295908 | C2 | semidirect |
| 8. #16812760 | C4 | semidirect |
| 9. #16812759 | C4 | semidirect |
| 17. C2×#13182012 | C4 | semidirect |
| 19. C22×#11724784 | C4 | semidirect |
| 20. C2×C8×D109 | C4 | semidirect |
| 22. C2×M16×C109 | C4 | semidirect |
| 94. C109 | #1757 | semidirect |
| 106. C2×M16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296012 | 2 |
| #20296005 | 2 |
| #20295989 | 2 |
| #20295908 | 2 |
| C2×#16812707 | 2 |
| #1757 | 109 |