Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 1. #20296050 | C2 | direct (N × H) |
| 2. C2×#16812766 | C2 | semidirect |
| 3. C2×C4⋊#11724786 | C2 | semidirect |
| 6. C2×#16812754 | C2 | semidirect |
| 7. C2×C4×#11724786 | C2 | semidirect |
| 13. #16812766 | C22 | semidirect |
| 14. C4⋊#11724786 | C22 | semidirect |
| 17. #16812754 | C22 | semidirect |
| 18. C4×#11724786 | C22 | semidirect |
| 98. C2×C109 | #433 | semidirect |
| 103. C109 | C2×#433 | semidirect |
| 201. C2 | #20296050 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296050 | 2 |
| C2×#16812766 | 2 |
| C2×C4⋊#11724786 | 2 |
| C2×C22⋊#11724786 | 2 |
| C2×#16812754 | 2 |
| C2×C4×#11724786 | 2 |
| C2×#16812655 | 2 |
| C2×#433 | 109 |