Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 2. C2×#16812728 | C2 | semidirect |
| 4. C4⋊Q8×D109 | C2 | semidirect |
| 5. #20295421 | C2 | semidirect |
| 6. #20295420 | C2 | semidirect |
| 7. #20295418 | C2 | semidirect |
| 8. #20295404 | C2 | semidirect |
| 9. #20295397 | C2 | semidirect |
| 10. #20294978 | C2 | semidirect |
| 11. #497×C109 | C2 | semidirect |
| 63. #13182012 | D4 | semidirect |
| 124. Dic109 | #137 | semidirect |
| 131. C109 | #3152 | semidirect |
| 139. #497 | 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×#16812728 | 2 |
| #20295575 | 2 |
| C4⋊Q8×D109 | 2 |
| #20295421 | 2 |
| #20295420 | 2 |
| #20295418 | 2 |
| #20295404 | 2 |
| #20295397 | 2 |
| #20294978 | 2 |
| #497×C109 | 2 |
| #3152 | 109 |