Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1026 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20275514 | C2 | semidirect |
| 2. #20273410 | C2 | semidirect |
| 3. #20273326 | C2 | semidirect |
| 4. #20273056 | C2 | semidirect |
| 6. #16810680 | C22 | semidirect |
| 7. C2×C4⋊#88322 | C22 | semidirect |
| 9. C2×#13133128 | C22 | semidirect |
| 191. C53 | #8456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275514 | 2 |
| #20273410 | 2 |
| #20273326 | 2 |
| #20273056 | 2 |
| C53×#3496 | 2 |
| #8456 | 53 |