Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20294924 | C2 | semidirect |
| 4. #20294915 | C2 | semidirect |
| 5. #20294888 | C2 | semidirect |
| 6. #20294885 | C2 | semidirect |
| 7. C4×C4⋊Dic109 | C2 | semidirect |
| 8. #376×C109 | C2 | semidirect |
| 11. C4×D436 | C4 | semidirect |
| 97. C109 | #2319 | semidirect |
| 105. #376 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D436 | 2 |
| #20294928 | 2 |
| #20294924 | 2 |
| #20294915 | 2 |
| #20294888 | 2 |
| #20294885 | 2 |
| C4×C4⋊Dic109 | 2 |
| #376×C109 | 2 |
| #2319 | 109 |