Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20289745 | C2 | semidirect |
| 4. #20289744 | C2 | semidirect |
| 112. C53 | #12005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291048 | 2 |
| D53⋊(C4⋊C16) | 2 |
| #20289745 | 2 |
| #20289744 | 2 |
| #20273000 | 2 |
| #12005 | 53 |