Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 124 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. #20289745 | C2 | semidirect |
| 64. #88322 | M32 | semidirect |
| 94. C53 | #12004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291047 | 2 |
| #20289745 | 2 |
| C2×C8×#88322 | 2 |
| #12004 | 53 |