Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20291536 | C2 | semidirect |
| 2. #20290202 | C2 | semidirect |
| 3. #20290054 | C2 | semidirect |
| 4. #20289975 | C2 | semidirect |
| 5. #20289622 | C2 | semidirect |
| 6. #20289583 | C2 | semidirect |
| 239. C53 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291536 | 2 |
| #20290202 | 2 |
| #20290054 | 2 |
| #20289975 | 2 |
| #20289622 | 2 |
| #20289583 | 2 |
| #20284854 | 2 |
| #9532 | 53 |