Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
260 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 114 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. #88324⋊C16 | C2 | semidirect |
| 4. #88324⋊C16 | C2 | semidirect |
| 5. #20289626 | C2 | semidirect |
| 6. C16×#88324 | C2 | semidirect |
| 130. C53 | #11412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291073 | 2 |
| #20289918 | 2 |
| #88324⋊C16 | 2 |
| #20289626 | 2 |
| C16×#88324 | 2 |
| #20276511 | 2 |
| #11412 | 53 |