Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 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. #22581527 | C2 | semidirect |
| 3. C2×#17984770 | C2 | semidirect |
| 4. #22580958 | C2 | semidirect |
| 5. C2×#17984761 | C2 | semidirect |
| 6. #22580713 | C2 | semidirect |
| 7. C2×#124×C139 | C2 | semidirect |
| 130. C139 | #2003 | semidirect |
| 134. C2×#124 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984868 | 2 |
| #22581527 | 2 |
| C2×#17984770 | 2 |
| #22580958 | 2 |
| C2×#17984761 | 2 |
| #22580713 | 2 |
| C2×#124×C139 | 2 |
| #2003 | 139 |