Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20280584 | C2 | semidirect |
| 3. #20273342 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20273159 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#3142 | C2 | semidirect |
| 197. #3142 | D53 | semidirect |
| 235. C53 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284802 | 2 |
| #20280584 | 2 |
| #20273342 | 2 |
| #20273262 | 2 |
| #20273159 | 2 |
| #20272580 | 2 |
| C53×#3142 | 2 |
| #10019 | 53 |