Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D109 | C2 | semidirect |
| 4. #20295405 | C2 | semidirect |
| 5. #20295266 | C2 | semidirect |
| 6. #20295237 | C2 | semidirect |
| 7. #20295183 | C2 | semidirect |
| 8. #20295180 | C2 | semidirect |
| 9. C4×#13182019 | C2 | semidirect |
| 11. #462×C109 | C2 | semidirect |
| 57. #13182019 | D4 | semidirect |
| 97. D436 | Q16 | semidirect |
| 114. C2×D109 | C2×Q16 | semidirect |
| 119. C4×C109 | C2×Q16 | semidirect |
| 131. C109 | D4×Q16 | semidirect |
| 138. #462 | D109 | semidirect |
| 254. C4 | Q16×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D109 | 2 |
| Q8×D436 | 2 |
| #20295691 | 2 |
| #20295405 | 2 |
| #20295266 | 2 |
| #20295237 | 2 |
| #20295183 | 2 |
| #20295180 | 2 |
| C4×#13182019 | 2 |
| #20295091 | 2 |
| #462×C109 | 2 |
| D4×Q16 | 109 |