Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4⋊Q8×D109 | C2 | semidirect |
| 3. #20295388 | C2 | semidirect |
| 4. #20295386 | C2 | semidirect |
| 5. #20295385 | C2 | semidirect |
| 6. #20295375 | C2 | semidirect |
| 7. #20295371 | C2 | semidirect |
| 8. #20295026 | C2 | semidirect |
| 9. #20295024 | C2 | semidirect |
| 10. #20294978 | C2 | semidirect |
| 11. #489×C109 | C2 | semidirect |
| 141. C109 | #3141 | semidirect |
| 147. #489 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295575 | 2 |
| C4⋊Q8×D109 | 2 |
| #20295388 | 2 |
| #20295386 | 2 |
| #20295385 | 2 |
| #20295375 | 2 |
| #20295371 | 2 |
| #20295026 | 2 |
| #20295024 | 2 |
| #20294978 | 2 |
| #489×C109 | 2 |
| #3141 | 109 |