Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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×#2178 | C2 | semidirect |
| 2. #11729263 | C2 | semidirect |
| 3. #11726814 | C2 | semidirect |
| 4. #11725389 | C2 | semidirect |
| 5. #11725316 | C2 | semidirect |
| 23. C7×Q32 | D4 | semidirect |
| 25. C7×D16 | D4 | semidirect |
| 37. #2178 | D7 | semidirect |
| 90. Q32 | D28 | semidirect |
| 95. D16 | D28 | semidirect |
| 148. C7 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2178 | 2 |
| #11729263 | 2 |
| #11726814 | 2 |
| #11725389 | 2 |
| #11725316 | 2 |
| #13692 | 7 |