Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊(C139⋊C8) | C2 | semidirect |
| 3. C2×#17984762 | C2 | semidirect |
| 4. C4×C4⋊C4×C139 | C2 | semidirect |
| 10. #17984839 | C4 | semidirect |
| 34. C4⋊C4×C139 | D4 | semidirect |
| 74. C4×C139 | #102 | semidirect |
| 84. C139 | #1982 | semidirect |
| 89. C4×C4⋊C4 | D139 | semidirect |
| 119. C4⋊C4 | D556 | semidirect |
| 159. C4 | #17984762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984839 | 2 |
| C2×C4⋊(C139⋊C8) | 2 |
| C2×#17984762 | 2 |
| C4×C4⋊C4×C139 | 2 |
| #1982 | 139 |