Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20295737 | C2 | semidirect |
| 3. #20295379 | C2 | semidirect |
| 4. #20295328 | C2 | semidirect |
| 5. #20295318 | C2 | semidirect |
| 6. #20295240 | C2 | semidirect |
| 8. C8×Dic218 | C2 | semidirect |
| 9. C4×#13182018 | C2 | semidirect |
| 10. #20295106 | C2 | semidirect |
| 11. #486×C109 | C2 | semidirect |
| 123. C109 | #3361 | semidirect |
| 127. #486 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295762 | 2 |
| #20295737 | 2 |
| #20295379 | 2 |
| #20295328 | 2 |
| #20295318 | 2 |
| #20295240 | 2 |
| #20295218 | 2 |
| C8×Dic218 | 2 |
| C4×#13182018 | 2 |
| #20295106 | 2 |
| #486×C109 | 2 |
| #3361 | 109 |