Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 10. Q8×#89137 | C4 | semidirect |
| 17. #16812762 | C4 | semidirect |
| 23. #16812624 | C4 | semidirect |
| 24. #16812623 | C4 | semidirect |
| 25. #16812622 | C4 | semidirect |
| 26. #103×C109 | C4 | semidirect |
| 74. Q8×C109 | C42 | semidirect |
| 92. Dic218 | C42 | semidirect |
| 106. #89137 | #103 | direct (N × H) |
| 123. C109 | C4×#103 | semidirect |
| 147. #103 | #89137 | direct (N × H) |
| 189. Q8 | C4×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#89137 | 2 |
| C2×#16812762 | 2 |
| C2×C8×#89137 | 2 |
| C4⋊C4×#89137 | 2 |
| #20295900 | 2 |
| #20295899 | 2 |
| #103×D109 | 2 |
| C4×#103 | 109 |