Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 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. #20285635 | C2 | semidirect |
| 2. #20285630 | C2 | semidirect |
| 3. #20285160 | C2 | semidirect |
| 4. #20275538 | C2 | semidirect |
| 5. #20273274 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 7. C53×#1517 | C2 | semidirect |
| 131. C2×#88322 | D8 | semidirect |
| 210. #1517 | D53 | semidirect |
| 243. C53 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285635 | 2 |
| #20285630 | 2 |
| #20285160 | 2 |
| #20275538 | 2 |
| #20273274 | 2 |
| #20272559 | 2 |
| C53×#1517 | 2 |
| #10218 | 53 |