Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
336 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#17984765 | C2 | semidirect |
| 4. C2×C4×C139⋊C8 | C2 | semidirect |
| 5. #382×C139 | C2 | semidirect |
| 10. #17984830 | C4 | semidirect |
| 78. C139 | #1958 | semidirect |
| 84. #382 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984830 | 2 |
| C2×#17984765 | 2 |
| C2×#17984762 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #382×C139 | 2 |
| #1958 | 139 |