Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16812731 | C2 | semidirect |
| 3. C2×Q16×D109 | C2 | semidirect |
| 4. #20295601 | C2 | semidirect |
| 5. #20295419 | C2 | semidirect |
| 6. #20295418 | C2 | semidirect |
| 7. #20295411 | C2 | semidirect |
| 8. #20295410 | C2 | semidirect |
| 9. #20295404 | C2 | semidirect |
| 10. #20294980 | C2 | semidirect |
| 11. #494×C109 | C2 | semidirect |
| 122. C109 | #3156 | semidirect |
| 132. #494 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812731 | 2 |
| C2×#16812722 | 2 |
| C2×Q16×D109 | 2 |
| #20295601 | 2 |
| #20295419 | 2 |
| #20295418 | 2 |
| #20295411 | 2 |
| #20295410 | 2 |
| #20295404 | 2 |
| #20294980 | 2 |
| #494×C109 | 2 |
| #3156 | 109 |