Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16811058 | C2 | semidirect |
| 2. #20285202 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276432 | C2 | semidirect |
| 5. #20275614 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 7. C53×#3414 | C2 | semidirect |
| 54. #13133157 | D4 | semidirect |
| 73. C2×Q16×C53 | D4 | semidirect |
| 77. C2×D8×C53 | D4 | semidirect |
| 85. C2×C16×C53 | D4 | semidirect |
| 211. #3414 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D53 | semidirect |
| 277. C2×D8 | C22⋊D53 | semidirect |
| 297. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| #20285202 | 2 |
| #20276451 | 2 |
| #20276432 | 2 |
| #20275614 | 2 |
| #20272800 | 2 |
| C53×#3414 | 2 |
| #13334 | 53 |