Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 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. C2×#17984786 | C2 | semidirect |
| 2. #22581194 | C2 | semidirect |
| 3. #22580754 | C2 | semidirect |
| 4. C22⋊(C139⋊C16) | C2 | semidirect |
| 6. C2×Dic556 | C22 | semidirect |
| 9. C2×C139⋊C16 | C22 | semidirect |
| 10. #17984776 | C22 | semidirect |
| 59. C22×C139 | SD32 | semidirect |
| 71. C139 | #2187 | semidirect |
| 131. C22 | #17984786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984786 | 2 |
| #22581194 | 2 |
| #22580754 | 2 |
| C22⋊(C139⋊C16) | 2 |
| C22×D8×C139 | 2 |
| #2187 | 139 |