Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22580706 | C2 | semidirect |
| 4. #22580704 | C2 | semidirect |
| 26. M16×C139 | C8 | semidirect |
| 49. C8×C139 | C2×C8 | semidirect |
| 66. C139 | #1565 | semidirect |
| 89. M16 | C139⋊C8 | semidirect |
| 116. C8 | C2×C139⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581006 | 2 |
| C2×C4⋊(C139⋊C8) | 2 |
| #22580706 | 2 |
| #22580704 | 2 |
| C4×M16×C139 | 2 |
| #1565 | 139 |