Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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×#16812786 | C2 | direct (N × H) |
| 2. C22×#13182039 | C2 | semidirect |
| 3. C22×#13182038 | C2 | semidirect |
| 4. C22×D109⋊C8 | C2 | semidirect |
| 5. C23×#11724786 | C2 | semidirect |
| 7. #16812786 | C22 | direct (N × H) |
| 8. C2×#13182039 | C22 | semidirect |
| 9. C2×#13182038 | C22 | semidirect |
| 10. C2×D109⋊C8 | C22 | semidirect |
| 14. C22×#11724786 | C22 | semidirect |
| 22. #13182039 | C23 | semidirect |
| 23. #13182038 | C23 | semidirect |
| 24. D109⋊C8 | C23 | semidirect |
| 28. C2×#11724786 | C23 | semidirect |
| 63. C22×C109 | #131 | semidirect |
| 73. C2×C109 | C2×#131 | semidirect |
| 77. C109 | C22×#131 | semidirect |
| 142. C22 | #16812786 | direct (N × H) |
| 151. C2 | C2×#16812786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812786 | 2 |
| C22×#13182039 | 2 |
| C22×#13182038 | 2 |
| C22×D109⋊C8 | 2 |
| C23×#11724786 | 2 |
| C22×#13182028 | 2 |
| C22×#131 | 109 |