Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581320 | C2 | semidirect |
| 4. #22581302 | C2 | semidirect |
| 100. C139 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581506 | 2 |
| C2×#17984840 | 2 |
| #22581320 | 2 |
| #22581302 | 2 |
| #22580963 | 2 |
| #22580962 | 2 |
| #22580961 | 2 |
| M16×Dic139 | 2 |
| #419×C139 | 2 |
| #3139 | 139 |