Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22581349 | C2 | semidirect |
| 3. #22581305 | C2 | semidirect |
| 6. C8×C139⋊C8 | C2 | semidirect |
| 7. #487×C139 | C2 | semidirect |
| 68. C139 | #1708 | semidirect |
| 73. #487 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581349 | 2 |
| #22581327 | 2 |
| #22581305 | 2 |
| #22581301 | 2 |
| #22581300 | 2 |
| C8×C139⋊C8 | 2 |
| #487×C139 | 2 |
| #1708 | 139 |