Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
486 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #11727736 | C2 | semidirect |
| 5. #11725493 | C2 | semidirect |
| 127. C23×C7 | #108 | semidirect |
| 146. C2×C4×C7 | #108 | semidirect |
| 267. C23 | #6396 | semidirect |
| 286. C2×C4 | #6396 | semidirect |
| 297. C7 | #8611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C7⋊C8 | 2 |
| C7×#1465 | 2 |
| #11729356 | 2 |
| #11727736 | 2 |
| #11725493 | 2 |
| #8611 | 7 |