Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285704 | C2 | semidirect |
| 2. #20285165 | C2 | semidirect |
| 3. #20280822 | C2 | semidirect |
| 4. #20273314 | C2 | semidirect |
| 5. #20273224 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1555 | C2 | semidirect |
| 41. #13133217 | D4 | semidirect |
| 42. #13133214 | D4 | semidirect |
| 60. #13133128 | D4 | semidirect |
| 73. C4⋊C8×C53 | D4 | semidirect |
| 208. #1555 | D53 | semidirect |
| 242. C53 | #10088 | semidirect |
| 279. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285704 | 2 |
| #20285165 | 2 |
| #20280822 | 2 |
| #20273314 | 2 |
| #20273224 | 2 |
| #20272607 | 2 |
| C53×#1555 | 2 |
| #10088 | 53 |