Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×#17984785 | C2 | semidirect |
| 3. #22581191 | C2 | semidirect |
| 4. #22580757 | C2 | semidirect |
| 5. #22580755 | C2 | semidirect |
| 6. (C2×D139)⋊C16 | C2 | semidirect |
| 7. C2×Q32×C139 | C2 | semidirect |
| 85. C139 | #2189 | semidirect |
| 88. C2×Q32 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C2×#17984785 | 2 |
| #22581191 | 2 |
| #22580757 | 2 |
| #22580755 | 2 |
| (C2×D139)⋊C16 | 2 |
| C2×Q32×C139 | 2 |
| #2189 | 139 |