Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
496 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 109 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. C7×#1979 | C2 | semidirect |
| 4. #11729815 | C2 | semidirect |
| 6. #11725535 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 17. C2×#6402 | C4 | semidirect |
| 34. C2×C7×Q16 | C2×C4 | semidirect |
| 64. C2×C7⋊C16 | C2×C4 | semidirect |
| 69. #1979 | D7 | semidirect |
| 173. C2×Q16 | C4×D7 | semidirect |
| 300. C7 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6402 | 2 |
| #11736006 | 2 |
| C7×#1979 | 2 |
| #11729815 | 2 |
| C2×#89290 | 2 |
| #11725535 | 2 |
| #11725477 | 2 |
| #13019 | 7 |