Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11739926 | C2 | semidirect |
| 5. #11729375 | C2 | semidirect |
| 6. #11728254 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 102. C2×C7×Q8 | SD16 | semidirect |
| 310. C2×Q8 | #1142 | semidirect |
| 410. C7 | #9999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3037 | 2 |
| #11740760 | 2 |
| #11739926 | 2 |
| #11729568 | 2 |
| #11729375 | 2 |
| #11728254 | 2 |
| #11725519 | 2 |
| #9999 | 7 |