Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 56. C8×C139 | Q16 | semidirect |
| 70. C139 | #1672 | semidirect |
| 127. C8 | Dic556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581351 | 2 |
| #22581249 | 2 |
| #22581164 | 2 |
| C8×Dic278 | 2 |
| #22580701 | 2 |
| #22580700 | 2 |
| #334×C139 | 2 |
| #1672 | 139 |