Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 1. C22×D848 | C2 | semidirect |
| 2. C2×#16810893 | C2 | semidirect |
| 3. #20284363 | C2 | semidirect |
| 4. C2×#16810437 | C2 | semidirect |
| 5. #20276432 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C2×C53×#350 | C2 | semidirect |
| 45. C2×D424 | D4 | semidirect |
| 55. #13133153 | D4 | semidirect |
| 74. C2×C16×C53 | D4 | semidirect |
| 198. C2×#350 | D53 | semidirect |
| 228. C53 | #13319 | semidirect |
| 268. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810893 | 2 |
| #20284363 | 2 |
| C2×#16810437 | 2 |
| #20276432 | 2 |
| #20272811 | 2 |
| C2×C53×#350 | 2 |
| #13319 | 53 |