Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #11729181 | C2 | semidirect |
| 5. C2×#89282 | C2 | semidirect |
| 6. C7×#1386 | C2 | semidirect |
| 7. #11725531 | C2 | semidirect |
| 22. #89310 | C4 | semidirect |
| 46. C7×M32 | C2×C4 | semidirect |
| 59. C2×C7⋊C16 | C2×C4 | semidirect |
| 68. #1386 | D7 | semidirect |
| 179. M32 | C4×D7 | semidirect |
| 284. C7 | #12934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736561 | 2 |
| #11729192 | 2 |
| #11729181 | 2 |
| #11728419 | 2 |
| C2×#89282 | 2 |
| C7×#1386 | 2 |
| #11725531 | 2 |
| #12934 | 7 |