Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #22580706 | C2 | semidirect |
| 3. #22580704 | C2 | semidirect |
| 60. C139 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581010 | 2 |
| #22580706 | 2 |
| #22580704 | 2 |
| C2×C4×C8×C139 | 2 |
| #1568 | 139 |