Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #20279714 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20273210 | C2 | semidirect |
| 5. #20273110 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#3037 | C2 | semidirect |
| 90. C2×Q8×C53 | D8 | semidirect |
| 221. #3037 | D53 | semidirect |
| 257. C53 | #10242 | semidirect |
| 317. C2×Q8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20279714 | 2 |
| #20273384 | 2 |
| #20273210 | 2 |
| #20273110 | 2 |
| #20272616 | 2 |
| C53×#3037 | 2 |
| #10242 | 53 |