Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C2×#89967 | C2 | semidirect |
| 3. C2×#89640 | C2 | semidirect |
| 4. C2×C7×#360 | C2 | semidirect |
| 5. #11729199 | C2 | semidirect |
| 6. C2×#89309 | C2 | semidirect |
| 7. #11725527 | C2 | semidirect |
| 58. C2×Dic28 | D4 | semidirect |
| 71. C7×#106 | D4 | semidirect |
| 79. #6386 | D4 | semidirect |
| 85. C2×#360 | D7 | semidirect |
| 263. #106 | C22⋊D7 | semidirect |
| 397. C7 | #13317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741360 | 2 |
| C2×#89967 | 2 |
| C2×#89640 | 2 |
| C2×C7×#360 | 2 |
| #11729199 | 2 |
| C2×#89309 | 2 |
| #11725527 | 2 |
| #13317 | 7 |