Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 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. Q8×Dic218 | C2 | semidirect |
| 4. #20295376 | C2 | semidirect |
| 6. #20295309 | C2 | semidirect |
| 8. #20295153 | C2 | semidirect |
| 9. #20295133 | C2 | semidirect |
| 11. #462×C109 | C2 | semidirect |
| 117. C109 | #3369 | semidirect |
| 125. #462 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic218 | 2 |
| #20295750 | 2 |
| #20295387 | 2 |
| #20295376 | 2 |
| #20295317 | 2 |
| #20295309 | 2 |
| #20295250 | 2 |
| #20295153 | 2 |
| #20295133 | 2 |
| C4×#13182016 | 2 |
| #462×C109 | 2 |
| #3369 | 109 |