Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#17984850 | C2 | semidirect |
| 3. #22581030 | C2 | semidirect |
| 4. #22581018 | C2 | semidirect |
| 5. #22580921 | C2 | semidirect |
| 6. C2×C4×C139⋊C8 | C2 | semidirect |
| 7. #423×C139 | C2 | semidirect |
| 34. C2×C139⋊C8 | D4 | semidirect |
| 75. C4×C139 | #131 | semidirect |
| 83. C139 | #2931 | semidirect |
| 89. #423 | D139 | semidirect |
| 160. C4 | #17984850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984850 | 2 |
| #22581503 | 2 |
| #22581030 | 2 |
| #22581018 | 2 |
| #22580921 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #423×C139 | 2 |
| #2931 | 139 |