Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #20289741 | C2 | semidirect |
| 4. #20289741 | C2 | semidirect |
| 5. #20289740 | C2 | semidirect |
| 6. #20289739 | C2 | semidirect |
| 123. C53 | #12028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290276 | 2 |
| D53⋊#334 | 2 |
| #20289741 | 2 |
| #20289740 | 2 |
| #20289739 | 2 |
| #20276517 | 2 |
| #12028 | 53 |