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 |
|---|---|---|
| 1. C7×#3414 | C2 | semidirect |
| 2. #11741349 | C2 | semidirect |
| 3. #11741339 | C2 | semidirect |
| 4. #11729839 | C2 | semidirect |
| 5. #11729834 | C2 | semidirect |
| 6. #11729202 | C2 | semidirect |
| 7. #11725617 | C2 | semidirect |
| 48. C2×C7×Q16 | D4 | semidirect |
| 52. C2×C7×D8 | D4 | semidirect |
| 82. C2×C7×C16 | D4 | semidirect |
| 95. C2×C7⋊C16 | D4 | semidirect |
| 97. #3414 | D7 | semidirect |
| 264. C2×Q16 | C22⋊D7 | semidirect |
| 273. C2×D8 | C22⋊D7 | semidirect |
| 297. C2×C16 | C22⋊D7 | semidirect |
| 443. C7 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| #11741349 | 2 |
| #11741339 | 2 |
| #11729839 | 2 |
| #11729834 | 2 |
| #11729202 | 2 |
| #11725617 | 2 |
| #13340 | 7 |