Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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. C22×Dic424 | C2 | semidirect |
| 4. #20283582 | C2 | semidirect |
| 5. #20276776 | C2 | semidirect |
| 6. #20276764 | C2 | semidirect |
| 7. #20276473 | C2 | semidirect |
| 8. #20276434 | C2 | semidirect |
| 206. C53 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| C22×Dic424 | 2 |
| #20285210 | 2 |
| #20283582 | 2 |
| #20276776 | 2 |
| #20276764 | 2 |
| #20276473 | 2 |
| #20276434 | 2 |
| C53×#2138 | 2 |
| #33588 | 53 |