Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #20295424 | C2 | semidirect |
| 4. #20295365 | C2 | semidirect |
| 5. #20295355 | C2 | semidirect |
| 6. #20295321 | C2 | semidirect |
| 7. #20295311 | C2 | semidirect |
| 8. #20295281 | C2 | semidirect |
| 10. #20295067 | C2 | semidirect |
| 11. C4×Q16×C109 | C2 | semidirect |
| 117. C109 | #3356 | semidirect |
| 126. C4×Q16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295749 | 2 |
| #20295736 | 2 |
| #20295424 | 2 |
| #20295365 | 2 |
| #20295355 | 2 |
| #20295321 | 2 |
| #20295311 | 2 |
| #20295281 | 2 |
| #20295105 | 2 |
| #20295067 | 2 |
| C4×Q16×C109 | 2 |
| #3356 | 109 |