Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 252. C7 | #10606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728278 | 2 |
| #11728274 | 2 |
| #11728262 | 2 |
| #11728248 | 2 |
| C2×#89277 | 2 |
| #11728174 | 2 |
| C7×#1292 | 2 |
| #10606 | 7 |