Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 1. C2×C7×#510 | C2 | semidirect |
| 3. C2×#89951 | C2 | semidirect |
| 4. C2×#89361 | C2 | semidirect |
| 5. #11729821 | C2 | semidirect |
| 6. C2×#89313 | C2 | semidirect |
| 7. #11725618 | C2 | semidirect |
| 47. C2×C7×Q16 | D4 | semidirect |
| 76. C7×M32 | D4 | semidirect |
| 87. #6386 | D4 | semidirect |
| 90. C2×#510 | D7 | semidirect |
| 251. C2×Q16 | C22⋊D7 | semidirect |
| 276. M32 | C22⋊D7 | semidirect |
| 417. C7 | #13342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#510 | 2 |
| #11741349 | 2 |
| C2×#89951 | 2 |
| C2×#89361 | 2 |
| #11729821 | 2 |
| C2×#89313 | 2 |
| #11725618 | 2 |
| #13342 | 7 |