Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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×#89698 | C2 | semidirect |
| 3. C7×#1749 | C2 | semidirect |
| 4. C2×#89259 | C2 | semidirect |
| 5. #11725465 | C2 | semidirect |
| 63. #6377 | D4 | semidirect |
| 66. #1749 | D7 | semidirect |
| 374. C7 | #9123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739522 | 2 |
| C2×#89698 | 2 |
| C7×#1749 | 2 |
| C2×#89259 | 2 |
| #11725465 | 2 |
| #9123 | 7 |