Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
640 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 2. C2×#16812766 | C2 | direct (N × H) |
| 6. #16812766 | C22 | direct (N × H) |
| 14. C22×Dic109 | C8 | semidirect |
| 32. C2×Dic109 | C2×C8 | semidirect |
| 39. C22×C109 | C4⋊C8 | semidirect |
| 46. Dic109 | C22×C8 | semidirect |
| 49. C2×C109 | C2×C4⋊C8 | semidirect |
| 54. C109 | C22×C4⋊C8 | semidirect |
| 93. C22 | #16812766 | direct (N × H) |
| 103. C2 | C2×#16812766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11724786 | 2 |
| C2×#16812766 | 2 |
| C22×C4×Dic109 | 2 |
| C22×C4⋊C8 | 109 |