Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22580996 | C2 | semidirect |
| 5. C2×#17984760 | C2 | semidirect |
| 6. #22580859 | C2 | semidirect |
| 7. #339×C139 | C2 | semidirect |
| 120. C139 | #2038 | semidirect |
| 128. #339 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581529 | 2 |
| #22580996 | 2 |
| C2×#17984770 | 2 |
| #22580955 | 2 |
| C2×#17984760 | 2 |
| #22580859 | 2 |
| #339×C139 | 2 |
| #2038 | 139 |