Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×Dic218 | C2 | semidirect |
| 3. #20295376 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 7. #20295233 | C2 | semidirect |
| 8. #20295157 | C2 | semidirect |
| 9. #20295131 | C2 | semidirect |
| 117. C109 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic218 | 2 |
| #20295385 | 2 |
| #20295376 | 2 |
| #20295316 | 2 |
| #20295311 | 2 |
| #20295245 | 2 |
| #20295233 | 2 |
| #20295157 | 2 |
| #20295131 | 2 |
| C4×#13182017 | 2 |
| #556×C109 | 2 |
| #3369 | 109 |