Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22581001 | C2 | semidirect |
| 2. #22580979 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 7. #424×C139 | C2 | semidirect |
| 89. C139 | #2098 | semidirect |
| 93. #424 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581001 | 2 |
| #22580979 | 2 |
| #22580971 | 2 |
| #22580969 | 2 |
| #22580919 | 2 |
| #22580709 | 2 |
| #424×C139 | 2 |
| #2098 | 139 |