Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295750 | C2 | semidirect |
| 3. #20295363 | C2 | semidirect |
| 4. #20295353 | C2 | semidirect |
| 5. #20295308 | C2 | semidirect |
| 6. #20295303 | C2 | semidirect |
| 7. #20295273 | C2 | semidirect |
| 8. C4×#13182018 | C2 | semidirect |
| 9. #20295105 | C2 | semidirect |
| 10. #20295067 | C2 | semidirect |
| 11. #500×C109 | C2 | semidirect |
| 98. C8×C109 | #41 | semidirect |
| 123. C109 | #3353 | semidirect |
| 126. #500 | D109 | semidirect |
| 222. C8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295750 | 2 |
| #20295679 | 2 |
| #20295363 | 2 |
| #20295353 | 2 |
| #20295308 | 2 |
| #20295303 | 2 |
| #20295273 | 2 |
| C4×#13182018 | 2 |
| #20295105 | 2 |
| #20295067 | 2 |
| #500×C109 | 2 |
| #3353 | 109 |