Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17984778 | C2 | semidirect |
| 5. #22580908 | C2 | semidirect |
| 6. #22580713 | C2 | semidirect |
| 7. #336×C139 | C2 | semidirect |
| 14. #17984767 | C4 | semidirect |
| 15. #17984767 | C4 | semidirect |
| 16. #17984764 | C4 | semidirect |
| 17. #17984764 | C4 | semidirect |
| 105. C139 | #1929 | semidirect |
| 113. #336 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984778 | 2 |
| C2×#17984770 | 2 |
| #22580950 | 2 |
| #22580919 | 2 |
| #22580908 | 2 |
| #22580713 | 2 |
| #336×C139 | 2 |
| #1929 | 139 |