Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #20295742 | C2 | semidirect |
| 2. #20295679 | C2 | semidirect |
| 3. #20295352 | C2 | semidirect |
| 4. #20295346 | C2 | semidirect |
| 5. #20295313 | C2 | semidirect |
| 6. #20295303 | C2 | semidirect |
| 7. #20295280 | C2 | semidirect |
| 8. C4×D872 | C2 | semidirect |
| 9. #20295105 | C2 | semidirect |
| 10. #20295065 | C2 | semidirect |
| 11. #498×C109 | C2 | semidirect |
| 100. C8×C109 | #41 | semidirect |
| 128. C109 | #3354 | semidirect |
| 131. #498 | D109 | semidirect |
| 229. C8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295742 | 2 |
| #20295679 | 2 |
| #20295352 | 2 |
| #20295346 | 2 |
| #20295313 | 2 |
| #20295303 | 2 |
| #20295280 | 2 |
| C4×D872 | 2 |
| #20295105 | 2 |
| #20295065 | 2 |
| #498×C109 | 2 |
| #3354 | 109 |