Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17984840 | C2 | semidirect |
| 4. #22580962 | C2 | semidirect |
| 5. C2×#17984760 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 125. C139 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581524 | 2 |
| C2×#17984840 | 2 |
| C2×#17984769 | 2 |
| #22580962 | 2 |
| C2×#17984760 | 2 |
| #22580714 | 2 |
| C2×#137×C139 | 2 |
| #2005 | 139 |