Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276462 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20275503 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 50. #13133153 | D4 | semidirect |
| 172. C2×#361 | D53 | semidirect |
| 201. C53 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285196 | 2 |
| #20276462 | 2 |
| C2×#16810436 | 2 |
| #20276444 | 2 |
| #20275503 | 2 |
| #20272802 | 2 |
| C2×C53×#361 | 2 |
| #13417 | 53 |