Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16810364 | C2 | semidirect |
| 4. #20273070 | C2 | semidirect |
| 5. #20272614 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 228. C53 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285879 | 2 |
| #20273335 | 2 |
| C2×#16810364 | 2 |
| #20273070 | 2 |
| #20272614 | 2 |
| #20272559 | 2 |
| C53×#2968 | 2 |
| #9266 | 53 |