Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #22581584 | C2 | semidirect |
| 4. #22580714 | C2 | semidirect |
| 5. #343×C139 | C2 | semidirect |
| 22. C2×D556 | Q8 | semidirect |
| 81. C139 | #2027 | semidirect |
| 86. #343 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22580959 | 2 |
| #22580854 | 2 |
| #22580714 | 2 |
| #343×C139 | 2 |
| #2027 | 139 |