Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20275691 | C2 | semidirect |
| 3. #20275544 | C2 | semidirect |
| 4. #20275542 | C2 | semidirect |
| 5. #20273452 | C2 | semidirect |
| 6. #20273448 | C2 | semidirect |
| 7. C53×#1560 | C2 | semidirect |
| 8. #16811367 | C4 | semidirect |
| 241. #1560 | D53 | semidirect |
| 274. C53 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289113 | 2 |
| #20275691 | 2 |
| #20275544 | 2 |
| #20275542 | 2 |
| #20273452 | 2 |
| #20273448 | 2 |
| C53×#1560 | 2 |
| #8532 | 53 |