Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 14. #17984775 | C4 | semidirect |
| 59. C139⋊C8 | C4⋊C4 | semidirect |
| 98. C139 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984775 | 2 |
| C2×#17984773 | 2 |
| C2×#17984752 | 2 |
| #22580852 | 2 |
| #22580849 | 2 |
| #22580716 | 2 |
| #340×C139 | 2 |
| #1943 | 139 |