Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#89680 | C2 | semidirect |
| 2. C2×#89669 | C2 | semidirect |
| 3. #11736595 | C2 | semidirect |
| 4. C2×#89310 | C2 | semidirect |
| 5. C2×#89292 | C2 | semidirect |
| 6. C2×#89286 | C2 | semidirect |
| 7. C7×#1387 | C2 | semidirect |
| 54. C2×D56 | D4 | semidirect |
| 68. C7×M32 | D4 | semidirect |
| 71. C7×#108 | D4 | semidirect |
| 88. #1387 | D7 | semidirect |
| 256. M32 | D28 | semidirect |
| 262. #108 | D28 | semidirect |
| 405. C7 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89680 | 2 |
| C2×#89669 | 2 |
| #11736595 | 2 |
| C2×#89310 | 2 |
| C2×#89292 | 2 |
| C2×#89286 | 2 |
| C7×#1387 | 2 |
| #13307 | 7 |