Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×Q8×Dic109 | C2 | semidirect |
| 3. #20295340 | C2 | semidirect |
| 4. #20295337 | C2 | semidirect |
| 5. #20295319 | C2 | semidirect |
| 6. #20295224 | C2 | semidirect |
| 7. #20295165 | C2 | semidirect |
| 8. #20295129 | C2 | semidirect |
| 9. #20295127 | C2 | semidirect |
| 10. #20295080 | C2 | semidirect |
| 11. #448×C109 | C2 | semidirect |
| 87. Q8×C109 | #41 | semidirect |
| 141. C109 | #3112 | semidirect |
| 149. #448 | D109 | semidirect |
| 229. Q8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295571 | 2 |
| C2×Q8×Dic109 | 2 |
| #20295340 | 2 |
| #20295337 | 2 |
| #20295319 | 2 |
| #20295224 | 2 |
| #20295165 | 2 |
| #20295129 | 2 |
| #20295127 | 2 |
| #20295080 | 2 |
| #448×C109 | 2 |
| #3112 | 109 |