Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #20295913 | C2 | semidirect |
| 4. C16×#89137 | C2 | semidirect |
| 8. #16812774 | C4 | semidirect |
| 9. #16812773 | C4 | semidirect |
| 16. #16812639 | C4 | semidirect |
| 17. #16812638 | C4 | semidirect |
| 19. M32×C109 | C4 | semidirect |
| 28. #13182032 | C2×C4 | semidirect |
| 35. #13182004 | C2×C4 | semidirect |
| 37. C16×C109 | C2×C4 | semidirect |
| 59. #89137 | M32 | direct (N × H) |
| 69. C109 | C4×M32 | semidirect |
| 82. M32 | #89137 | direct (N × H) |
| 106. C16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊M32 | 2 |
| C2×C8×#89137 | 2 |
| #20295913 | 2 |
| C16×#89137 | 2 |
| M32×D109 | 2 |
| C4×M32 | 109 |