Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #20295761 | C2 | semidirect |
| 2. #20295733 | C2 | semidirect |
| 3. #20295382 | C2 | semidirect |
| 4. #20295373 | C2 | semidirect |
| 5. #20295325 | C2 | semidirect |
| 6. #20295321 | C2 | semidirect |
| 7. #20295243 | C2 | semidirect |
| 9. C8×Dic218 | C2 | semidirect |
| 10. #20295106 | C2 | semidirect |
| 11. C4×SD16×C109 | C2 | semidirect |
| 123. C109 | #3361 | semidirect |
| 133. C4×SD16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295761 | 2 |
| #20295733 | 2 |
| #20295382 | 2 |
| #20295373 | 2 |
| #20295325 | 2 |
| #20295321 | 2 |
| #20295243 | 2 |
| #20295221 | 2 |
| C8×Dic218 | 2 |
| #20295106 | 2 |
| C4×SD16×C109 | 2 |
| #3361 | 109 |