Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295733 | C2 | semidirect |
| 2. #20295697 | C2 | semidirect |
| 3. #20295389 | C2 | semidirect |
| 4. #20295373 | C2 | semidirect |
| 5. #20295329 | C2 | semidirect |
| 6. #20295316 | C2 | semidirect |
| 7. #20295221 | C2 | semidirect |
| 8. #20295219 | C2 | semidirect |
| 9. #20295156 | C2 | semidirect |
| 10. #20295135 | C2 | semidirect |
| 11. C4×D8×C109 | C2 | semidirect |
| 80. D4×C109 | #41 | semidirect |
| 130. C109 | #3366 | semidirect |
| 141. C4×D8 | D109 | semidirect |
| 218. D4 | #13182029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295733 | 2 |
| #20295697 | 2 |
| #20295389 | 2 |
| #20295373 | 2 |
| #20295329 | 2 |
| #20295316 | 2 |
| #20295221 | 2 |
| #20295219 | 2 |
| #20295156 | 2 |
| #20295135 | 2 |
| C4×D8×C109 | 2 |
| #3366 | 109 |