Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 8. #17984778 | C4 | semidirect |
| 9. #17984776 | C4 | semidirect |
| 10. #17984774 | C4 | semidirect |
| 16. #97×C139 | C4 | semidirect |
| 62. C139 | #1773 | semidirect |
| 78. #97 | Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984778 | 2 |
| #22580991 | 2 |
| #22580908 | 2 |
| #22580713 | 2 |
| C2×#97×C139 | 2 |
| #1773 | 139 |