Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1254 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#4478 | C2 | direct (N × H) |
| 21. #4478 | C22 | direct (N × H) |
| 250. C22×C3 | #356 | semidirect |
| 300. C2×C3 | C2×#356 | semidirect |
| 304. C22 | #4478 | direct (N × H) |
| 316. C3 | C22×#356 | semidirect |
| 319. C2 | C2×#4478 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#944 | 2 |
| C22×C3×#101 | 2 |
| C22×#836 | 2 |
| C2×#4478 | 2 |
| C22×#356 | 3 |