Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20275488 | C2 | semidirect |
| 5. #20273118 | C2 | semidirect |
| 6. #20272565 | C2 | semidirect |
| 7. C53×#1550 | C2 | semidirect |
| 173. #1550 | D53 | semidirect |
| 203. C53 | #10553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285091 | 2 |
| #20275488 | 2 |
| #20273384 | 2 |
| C2×#16810366 | 2 |
| #20273118 | 2 |
| #20272565 | 2 |
| C53×#1550 | 2 |
| #10553 | 53 |