Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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×#89951 | C2 | semidirect |
| 2. C22×#6402 | C2 | semidirect |
| 4. C7×#1979 | C2 | semidirect |
| 5. C2×#89292 | C2 | semidirect |
| 6. C2×#89290 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 40. C2×C7×Q16 | D4 | semidirect |
| 76. #6386 | D4 | semidirect |
| 80. C2×C7⋊C16 | D4 | semidirect |
| 86. #1979 | D7 | semidirect |
| 224. C2×Q16 | D28 | semidirect |
| 379. C7 | #13338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89951 | 2 |
| C22×#6402 | 2 |
| #11736010 | 2 |
| C7×#1979 | 2 |
| C2×#89292 | 2 |
| C2×#89290 | 2 |
| #11725477 | 2 |
| #13338 | 7 |