Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22581357 | C2 | semidirect |
| 3. #22580755 | C2 | semidirect |
| 4. #22580754 | C2 | semidirect |
| 5. #22580753 | C2 | semidirect |
| 6. C16×Dic139 | C2 | semidirect |
| 7. #357×C139 | C2 | semidirect |
| 72. C139 | #2240 | semidirect |
| 79. #357 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581357 | 2 |
| #22581328 | 2 |
| #22580755 | 2 |
| #22580754 | 2 |
| #22580753 | 2 |
| C16×Dic139 | 2 |
| #357×C139 | 2 |
| #2240 | 139 |