Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20295283 | C2 | semidirect |
| 5. #20295282 | C2 | semidirect |
| 6. #20295268 | C2 | semidirect |
| 7. #20295267 | C2 | semidirect |
| 8. #20295264 | C2 | semidirect |
| 9. #20295063 | C2 | semidirect |
| 10. #20295033 | C2 | semidirect |
| 11. #467×C109 | C2 | semidirect |
| 138. C109 | #3059 | semidirect |
| 147. #467 | 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 |
| C2×#16812705 | 2 |
| #20295599 | 2 |
| #20295283 | 2 |
| #20295282 | 2 |
| #20295268 | 2 |
| #20295267 | 2 |
| #20295264 | 2 |
| #20295063 | 2 |
| #20295033 | 2 |
| #467×C109 | 2 |
| #3059 | 109 |