Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
984 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 335 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. #11729364 | C2 | semidirect |
| 3. #11727147 | C2 | semidirect |
| 15. C7×#127 | C8 | semidirect |
| 32. C2×C7×D4 | C2×C8 | semidirect |
| 43. C42×C7 | C2×C8 | semidirect |
| 73. #127 | C7⋊C8 | semidirect |
| 95. C2×D4 | C2×C7⋊C8 | semidirect |
| 108. C42 | C2×C7⋊C8 | semidirect |
| 128. C7 | #23355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#127 | 2 |
| #11729364 | 2 |
| #11727147 | 2 |
| #23355 | 7 |