Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1230 conjugacy classes of subgroups; only the 367 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 367 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×#89784 | C2 | semidirect |
| 3. #11729368 | C2 | semidirect |
| 4. #11727148 | C2 | semidirect |
| 5. C42×C7⋊C8 | C2 | semidirect |
| 35. C4×C7⋊C8 | D4 | semidirect |
| 54. C42×C7 | M16 | semidirect |
| 90. C7⋊C8 | #127 | semidirect |
| 117. C4×C7 | #436 | semidirect |
| 138. C42 | #1136 | semidirect |
| 163. C7 | #21681 | semidirect |
| 172. C4 | #89784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#127 | 2 |
| C2×#89784 | 2 |
| #11729368 | 2 |
| #11727148 | 2 |
| C42×C7⋊C8 | 2 |
| #21681 | 7 |