Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #20295762 | C2 | semidirect |
| 2. #20295696 | C2 | semidirect |
| 3. #20295414 | C2 | semidirect |
| 4. #20295239 | C2 | semidirect |
| 5. #20295223 | C2 | semidirect |
| 6. #20295219 | C2 | semidirect |
| 7. #20295218 | C2 | semidirect |
| 8. #20295156 | C2 | semidirect |
| 9. #20295138 | C2 | semidirect |
| 10. C4×#13182018 | C2 | semidirect |
| 11. #493×C109 | C2 | semidirect |
| 107. C8×C109 | #41 | semidirect |
| 135. C109 | #3399 | semidirect |
| 139. #493 | D109 | semidirect |
| 243. C8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295762 | 2 |
| #20295696 | 2 |
| #20295414 | 2 |
| #20295239 | 2 |
| #20295223 | 2 |
| #20295219 | 2 |
| #20295218 | 2 |
| #20295156 | 2 |
| #20295138 | 2 |
| C4×#13182018 | 2 |
| #493×C109 | 2 |
| #3399 | 109 |