Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
232 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 110 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. #20289744 | C2 | semidirect |
| 4. #20289737 | C2 | semidirect |
| 69. C8×C53 | M32 | semidirect |
| 109. C53 | #12017 | semidirect |
| 167. C8 | #13133291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291076 | 2 |
| #20291047 | 2 |
| #20289744 | 2 |
| #20289737 | 2 |
| M16×#88322 | 2 |
| #12017 | 53 |