Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#16812758 | C2 | semidirect |
| 2. #20295932 | C2 | semidirect |
| 3. #20295930 | C2 | semidirect |
| 9. #16812695 | C4 | semidirect |
| 11. #16812688 | C4 | semidirect |
| 15. #16812658 | C4 | semidirect |
| 16. C2×#41×C109 | C4 | semidirect |
| 31. C4×Dic109 | C2×C4 | semidirect |
| 32. C4×Dic109 | C2×C4 | semidirect |
| 34. C2×Q8×C109 | C2×C4 | semidirect |
| 36. C2×D4×C109 | C2×C4 | semidirect |
| 87. C109 | #2127 | semidirect |
| 92. C2×#41 | #89137 | semidirect |
| 106. C2×Q8 | C2×#89137 | semidirect |
| 114. C2×D4 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812758 | 2 |
| #20295932 | 2 |
| #20295930 | 2 |
| #20295590 | 2 |
| #2127 | 109 |