Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #22581239 | C2 | direct (N × H) |
| 27. C2×Dic278 | Q8 | semidirect |
| 49. Dic278 | C2×Q8 | semidirect |
| 78. C2×C139 | #475 | semidirect |
| 82. C139 | C2×#475 | semidirect |
| 161. C2 | #22581239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984842 | 2 |
| C2×C4×Dic278 | 2 |
| #22581239 | 2 |
| C2×#17984774 | 2 |
| C2×#17984767 | 2 |
| C2×C4⋊C8×C139 | 2 |
| C2×#475 | 139 |