Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16812698 | C2 | semidirect |
| 3. #20295384 | C2 | direct (N × H) |
| 4. C2×#16812624 | C2 | semidirect |
| 5. C2×#16812622 | C2 | semidirect |
| 7. C2×#16812609 | C2 | semidirect |
| 13. #16812698 | C22 | semidirect |
| 21. #16812624 | C22 | semidirect |
| 22. #16812622 | C22 | semidirect |
| 24. #16812609 | C22 | semidirect |
| 104. C2×C109 | #489 | semidirect |
| 109. C109 | C2×#489 | semidirect |
| 213. C2 | #20295384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812698 | 2 |
| C2×#16812686 | 2 |
| #20295384 | 2 |
| C2×#16812624 | 2 |
| C2×#16812622 | 2 |
| C2×#16812620 | 2 |
| C2×#16812609 | 2 |
| C2×#102×C109 | 2 |
| C2×#489 | 109 |