Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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. C7×#1749 | C2 | semidirect |
| 3. #11729283 | C2 | semidirect |
| 4. C2×#89259 | C2 | semidirect |
| 16. C2×C7×#97 | C22 | semidirect |
| 18. C2×#6377 | C22 | semidirect |
| 63. #1749 | D7 | semidirect |
| 136. C2×#97 | C2×D7 | semidirect |
| 239. C22×C7 | #329 | semidirect |
| 384. C7 | #8334 | semidirect |
| 399. C22 | #89259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6438 | 2 |
| C7×#1749 | 2 |
| #11729283 | 2 |
| C2×#89259 | 2 |
| #8334 | 7 |