Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #20296094 | C2 | direct (N × H) |
| 2. C2×Q8×#89137 | C2 | semidirect |
| 5. Q8×#89137 | C22 | semidirect |
| 10. C22×Dic218 | C4 | semidirect |
| 11. C2×Q8×D109 | C4 | semidirect |
| 12. C2×Q8×D109 | C4 | semidirect |
| 16. C22×Q8×C109 | C4 | semidirect |
| 23. C2×Dic218 | C2×C4 | semidirect |
| 25. Q8×D109 | C2×C4 | semidirect |
| 33. C2×Q8×C109 | C2×C4 | semidirect |
| 66. C2×C109 | #519 | semidirect |
| 69. D109 | #519 | semidirect |
| 72. C109 | C2×#519 | semidirect |
| 82. C22×Q8 | #89137 | semidirect |
| 96. C2×Q8 | C2×#89137 | semidirect |
| 141. C2 | #20296094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296094 | 2 |
| C2×Q8×#89137 | 2 |
| C2×#16812778 | 2 |
| C22×Q8×D109 | 2 |
| C2×#519 | 109 |