Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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. C2×#90001 | C2 | semidirect |
| 5. #11734304 | C2 | direct (N × H) |
| 6. C2×#89432 | C2 | semidirect |
| 15. #90001 | C22 | semidirect |
| 21. #89432 | C22 | semidirect |
| 175. C2×C7 | #2835 | semidirect |
| 203. C7 | C2×#2835 | semidirect |
| 219. C2 | #11734304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#393 | 2 |
| C2×#90001 | 2 |
| C2×#89725 | 2 |
| C2×#89718 | 2 |
| #11734304 | 2 |
| C2×#89432 | 2 |
| C2×#2835 | 7 |