Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 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. #22581332 | C2 | semidirect |
| 3. #22581301 | C2 | semidirect |
| 4. #22581300 | C2 | semidirect |
| 5. #22581299 | C2 | semidirect |
| 6. C8×C139⋊C8 | C2 | semidirect |
| 7. #486×C139 | C2 | semidirect |
| 74. C139 | #1709 | semidirect |
| 81. #486 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581332 | 2 |
| #22581329 | 2 |
| #22581301 | 2 |
| #22581300 | 2 |
| #22581299 | 2 |
| C8×C139⋊C8 | 2 |
| #486×C139 | 2 |
| #1709 | 139 |