Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20275853 | C2 | semidirect |
| 3. #20275815 | C2 | semidirect |
| 4. #20272540 | C2 | semidirect |
| 5. #20272540 | C2 | semidirect |
| 71. C2×D4×C53 | Q16 | semidirect |
| 231. C53 | #7782 | semidirect |
| 284. C2×D4 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282661 | 2 |
| #20275853 | 2 |
| #20275815 | 2 |
| #20272540 | 2 |
| #20272536 | 2 |
| C53×#2023 | 2 |
| #7782 | 53 |