Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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×#17984773 | C2 | semidirect |
| 3. C2×#17984764 | C2 | semidirect |
| 4. C2×#17984762 | C2 | semidirect |
| 5. C2×(C2×D139)⋊C8 | C2 | semidirect |
| 6. #22580810 | C2 | semidirect |
| 7. #340×C139 | C2 | semidirect |
| 46. C2×C139⋊C8 | D4 | semidirect |
| 143. C139 | #2034 | semidirect |
| 151. #340 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984817 | 2 |
| C2×#17984773 | 2 |
| C2×#17984764 | 2 |
| C2×#17984762 | 2 |
| C2×(C2×D139)⋊C8 | 2 |
| #22580810 | 2 |
| #340×C139 | 2 |
| #2034 | 139 |