Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16812690 | C2 | semidirect |
| 3. #20295324 | C2 | direct (N × H) |
| 4. C2×#16812633 | C2 | semidirect |
| 5. C2×#16812630 | C2 | semidirect |
| 6. C2×#16812628 | C2 | semidirect |
| 12. #16812690 | C22 | semidirect |
| 21. #16812633 | C22 | semidirect |
| 22. #16812630 | C22 | semidirect |
| 23. #16812628 | C22 | semidirect |
| 99. C2×C109 | #478 | semidirect |
| 104. C109 | C2×#478 | semidirect |
| 203. C2 | #20295324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812690 | 2 |
| C2×D4×Dic109 | 2 |
| #20295324 | 2 |
| C2×#16812633 | 2 |
| C2×#16812630 | 2 |
| C2×#16812628 | 2 |
| C2×#16812620 | 2 |
| C2×#102×C109 | 2 |
| C2×#478 | 109 |