Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
814 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 251 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. #11729066 | C2 | direct (N × H) |
| 102. C2×C4×C7 | Q32 | semidirect |
| 147. C4×C7 | C2×Q32 | semidirect |
| 179. C2×C7 | #2247 | semidirect |
| 193. C2×C4 | #6403 | semidirect |
| 202. C7 | C2×#2247 | semidirect |
| 209. C4 | C2×#6403 | semidirect |
| 212. C2 | #11729066 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#494 | 2 |
| C22×#6403 | 2 |
| C2×#89471 | 2 |
| #11729066 | 2 |
| C2×C4×C7⋊C16 | 2 |
| C2×#2247 | 7 |