Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20290354 | C2 | semidirect |
| 3. #20289746 | C2 | semidirect |
| 4. #20289672 | C2 | semidirect |
| 6. #88324⋊C16 | C2 | semidirect |
| 128. C53 | #12074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290354 | 2 |
| D8×#88324 | 2 |
| #20289746 | 2 |
| #20289672 | 2 |
| #20289669 | 2 |
| #88324⋊C16 | 2 |
| #20276570 | 2 |
| #12074 | 53 |