Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #20295507 | C2 | semidirect |
| 3. C2×#16812625 | C2 | semidirect |
| 4. #20295032 | C2 | semidirect |
| 5. #20294927 | C2 | semidirect |
| 6. #20294787 | C2 | semidirect |
| 7. #343×C109 | C2 | semidirect |
| 11. #16812727 | C4 | semidirect |
| 39. C2×D436 | C2×C4 | semidirect |
| 62. M16×C109 | C2×C4 | semidirect |
| 95. D436 | C22⋊C4 | semidirect |
| 100. Dic218 | C22⋊C4 | semidirect |
| 133. C109 | #1883 | semidirect |
| 139. #343 | D109 | semidirect |
| 185. M16 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812727 | 2 |
| #20295507 | 2 |
| C2×#16812625 | 2 |
| #20295032 | 2 |
| #20294927 | 2 |
| #20294787 | 2 |
| #343×C109 | 2 |
| #1883 | 109 |