Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20272831 | C2 | semidirect |
| 4. #20272795 | C2 | semidirect |
| 5. C53×#3162 | C2 | semidirect |
| 20. C2×Dic212 | Q8 | semidirect |
| 22. C2×D424 | Q8 | semidirect |
| 114. #3162 | D53 | semidirect |
| 135. C53 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276450 | 2 |
| #20275608 | 2 |
| #20272831 | 2 |
| #20272795 | 2 |
| C53×#3162 | 2 |
| #13373 | 53 |