Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 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. #20287849 | C2 | semidirect |
| 2. C2×#16811058 | C2 | semidirect |
| 3. #20285201 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20276430 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#1976 | C2 | semidirect |
| 65. #13133157 | D4 | semidirect |
| 67. C2×#11719908 | D4 | semidirect |
| 73. C2×Q16×C53 | D4 | semidirect |
| 75. C2×D8×C53 | D4 | semidirect |
| 216. #1976 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
| 265. C2×Q16 | D212 | semidirect |
| 277. C2×D8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| C2×#16811058 | 2 |
| #20285201 | 2 |
| #20276450 | 2 |
| #20276430 | 2 |
| #20272801 | 2 |
| C53×#1976 | 2 |
| #13334 | 53 |