Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C23×#1136 | C2 | semidirect |
| 3. C22×#6407 | C2 | direct (N × H) |
| 11. C22×#1136 | C22 | semidirect |
| 13. C2×#6407 | C22 | direct (N × H) |
| 31. C2×#1136 | C23 | semidirect |
| 33. #6407 | C23 | direct (N × H) |
| 60. #1136 | C24 | semidirect |
| 79. C23×C7 | #100 | semidirect |
| 118. C22×C7 | C2×#100 | semidirect |
| 152. C2×C7 | C22×#100 | semidirect |
| 161. C23 | #6407 | direct (N × H) |
| 175. C7 | C23×#100 | semidirect |
| 182. C22 | C2×#6407 | direct (N × H) |
| 191. C2 | C22×#6407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×D4 | 2 |
| C23×#1136 | 2 |
| C22×#6407 | 2 |
| C23×#100 | 7 |