Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16812718 | C2 | semidirect |
| 2. C2×Q16×D109 | C2 | semidirect |
| 3. #20295684 | C2 | semidirect |
| 4. #20295264 | C2 | semidirect |
| 5. #20295259 | C2 | semidirect |
| 6. #20295245 | C2 | semidirect |
| 7. #20295185 | C2 | semidirect |
| 8. #20295163 | C2 | semidirect |
| 9. C4×Dic436 | C2 | semidirect |
| 10. C8×D436 | C2 | semidirect |
| 11. #495×C109 | C2 | semidirect |
| 54. Dic436 | D4 | semidirect |
| 120. C2×D109 | #135 | semidirect |
| 137. C109 | #3285 | semidirect |
| 141. #495 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812718 | 2 |
| C2×Q16×D109 | 2 |
| #20295684 | 2 |
| #20295264 | 2 |
| #20295259 | 2 |
| #20295245 | 2 |
| #20295185 | 2 |
| #20295163 | 2 |
| C4×Dic436 | 2 |
| C8×D436 | 2 |
| #495×C109 | 2 |
| #3285 | 109 |