Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20295504 | C2 | semidirect |
| 4. #20295250 | C2 | semidirect |
| 5. #20295234 | C2 | semidirect |
| 6. #20295052 | C2 | semidirect |
| 7. #20295035 | C2 | semidirect |
| 9. C22×Q16×C109 | C2 | semidirect |
| 112. C109 | #3044 | semidirect |
| 114. C22×Q16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| #20295600 | 2 |
| #20295504 | 2 |
| #20295250 | 2 |
| #20295234 | 2 |
| #20295052 | 2 |
| #20295035 | 2 |
| #20295023 | 2 |
| C22×Q16×C109 | 2 |
| #3044 | 109 |