Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20295074 | C2 | semidirect |
| 2. #20295043 | C2 | semidirect |
| 3. #20295031 | C2 | semidirect |
| 4. #20295010 | C2 | semidirect |
| 5. C2×#16812616 | C2 | semidirect |
| 6. #20294798 | C2 | semidirect |
| 111. C109 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295074 | 2 |
| #20295043 | 2 |
| #20295031 | 2 |
| #20295010 | 2 |
| C2×#16812616 | 2 |
| #20294798 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #2048 | 109 |