Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22581310 | C2 | semidirect |
| 3. #22581305 | C2 | semidirect |
| 4. #22581301 | C2 | semidirect |
| 5. #22580947 | C2 | semidirect |
| 6. C2×C4×C139⋊C8 | C2 | semidirect |
| 7. #533×C139 | C2 | semidirect |
| 78. C139 | #3131 | semidirect |
| 80. #533 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22581310 | 2 |
| #22581305 | 2 |
| #22581301 | 2 |
| #22580947 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #533×C139 | 2 |
| #3131 | 139 |