Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 3. C2×#89300 | C2 | semidirect |
| 5. #11728403 | C2 | semidirect |
| 6. C7×#1382 | C2 | semidirect |
| 7. #11725538 | C2 | semidirect |
| 22. #89303 | C4 | semidirect |
| 47. C2×C7×C16 | C2×C4 | semidirect |
| 60. #6386 | C2×C4 | semidirect |
| 70. #1382 | D7 | semidirect |
| 183. C2×C16 | C4×D7 | semidirect |
| 291. C7 | #12926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736624 | 2 |
| C2×#89303 | 2 |
| C2×#89300 | 2 |
| #11728475 | 2 |
| #11728403 | 2 |
| C7×#1382 | 2 |
| #11725538 | 2 |
| #12926 | 7 |