Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295761 | C2 | semidirect |
| 2. #20295698 | C2 | semidirect |
| 3. #20295415 | C2 | semidirect |
| 4. #20295403 | C2 | semidirect |
| 5. #20295242 | C2 | semidirect |
| 6. #20295227 | C2 | semidirect |
| 7. #20295222 | C2 | semidirect |
| 8. #20295222 | C2 | semidirect |
| 9. #20295139 | C2 | semidirect |
| 10. C4×#13182018 | C2 | semidirect |
| 11. #446×C109 | C2 | semidirect |
| 108. C8×C109 | #41 | semidirect |
| 135. C109 | #3399 | semidirect |
| 144. #446 | D109 | semidirect |
| 243. C8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295761 | 2 |
| #20295698 | 2 |
| #20295415 | 2 |
| #20295403 | 2 |
| #20295242 | 2 |
| #20295227 | 2 |
| #20295222 | 2 |
| #20295139 | 2 |
| C4×#13182018 | 2 |
| #446×C109 | 2 |
| #3399 | 109 |