Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22581719 | C2 | semidirect |
| 3. #22580969 | C2 | semidirect |
| 4. #22580959 | C2 | semidirect |
| 5. C2×#17984758 | C2 | semidirect |
| 6. #22580724 | C2 | semidirect |
| 7. #338×C139 | C2 | semidirect |
| 12. C2×#14555774 | C4 | semidirect |
| 13. C2×D1112 | C4 | semidirect |
| 112. C139 | #1903 | semidirect |
| 120. #338 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984870 | 2 |
| #22581719 | 2 |
| #22580969 | 2 |
| #22580959 | 2 |
| C2×#17984758 | 2 |
| #22580724 | 2 |
| #338×C139 | 2 |
| #1903 | 139 |