Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #20295749 | C2 | semidirect |
| 2. #20295736 | C2 | semidirect |
| 3. #20295381 | C2 | semidirect |
| 4. #20295377 | C2 | semidirect |
| 5. #20295334 | C2 | semidirect |
| 6. #20295317 | C2 | semidirect |
| 8. #20295232 | C2 | semidirect |
| 9. C4×#13182018 | C2 | semidirect |
| 11. C8×Q8×C109 | C2 | semidirect |
| 121. C109 | #3360 | semidirect |
| 130. C8×Q8 | 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 |
| #20295381 | 2 |
| #20295377 | 2 |
| #20295334 | 2 |
| #20295317 | 2 |
| #20295242 | 2 |
| #20295232 | 2 |
| C4×#13182018 | 2 |
| C4×D872 | 2 |
| C8×Q8×C109 | 2 |
| #3360 | 109 |