Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C4×Q8×D109 | C2 | semidirect |
| 4. #20295251 | C2 | semidirect |
| 5. #20295250 | C2 | semidirect |
| 6. #20295233 | C2 | semidirect |
| 7. #20295227 | C2 | semidirect |
| 8. #20295226 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 10. #20295026 | C2 | semidirect |
| 11. #462×C109 | C2 | semidirect |
| 49. Q8×D109 | D4 | semidirect |
| 133. C4×C109 | #137 | semidirect |
| 147. C109 | #3037 | semidirect |
| 154. #462 | D109 | semidirect |
| 285. C4 | #16812731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812731 | 2 |
| #20295577 | 2 |
| C4×Q8×D109 | 2 |
| #20295251 | 2 |
| #20295250 | 2 |
| #20295233 | 2 |
| #20295227 | 2 |
| #20295226 | 2 |
| #20295048 | 2 |
| #20295026 | 2 |
| #462×C109 | 2 |
| #3037 | 109 |