Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20295378 | C2 | semidirect |
| 3. #20295361 | C2 | semidirect |
| 4. #20295318 | C2 | semidirect |
| 5. #20295265 | C2 | semidirect |
| 6. #20295236 | C2 | semidirect |
| 7. #20295181 | C2 | semidirect |
| 8. C4×#13182019 | C2 | semidirect |
| 10. C2×#16812622 | C2 | semidirect |
| 80. D4×C109 | Q16 | semidirect |
| 123. C109 | #3299 | semidirect |
| 208. D4 | #13182019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic218 | 2 |
| #20295378 | 2 |
| #20295361 | 2 |
| #20295318 | 2 |
| #20295265 | 2 |
| #20295236 | 2 |
| #20295181 | 2 |
| C4×#13182019 | 2 |
| D4×#11724784 | 2 |
| C2×#16812622 | 2 |
| #554×C109 | 2 |
| #3299 | 109 |