Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22581013 | C2 | semidirect |
| 3. #22581009 | C2 | semidirect |
| 4. #22580980 | C2 | semidirect |
| 7. M16×Dic139 | C2 | semidirect |
| 8. C2×#17984752 | C2 | semidirect |
| 9. #424×C139 | C2 | semidirect |
| 93. C139 | #2923 | semidirect |
| 99. #424 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581421 | 2 |
| #22581013 | 2 |
| #22581009 | 2 |
| #22580980 | 2 |
| #22580921 | 2 |
| #22580919 | 2 |
| M16×Dic139 | 2 |
| C2×#17984752 | 2 |
| #424×C139 | 2 |
| #2923 | 139 |