Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22580773 | C2 | semidirect |
| 4. #22580731 | C2 | semidirect |
| 5. #347×C139 | C2 | semidirect |
| 51. C139 | #2165 | semidirect |
| 57. #347 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580905 | 2 |
| #22580773 | 2 |
| #22580734 | 2 |
| #22580731 | 2 |
| #347×C139 | 2 |
| #2165 | 139 |