Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11739379 | C2 | semidirect |
| 3. C7×#2240 | C2 | semidirect |
| 4. #11729139 | C2 | semidirect |
| 5. #11729045 | C2 | semidirect |
| 6. #11726950 | C2 | semidirect |
| 7. #11726929 | C2 | semidirect |
| 8. #11726819 | C2 | semidirect |
| 9. C4×D7×C16 | C2 | semidirect |
| 80. #2240 | D7 | semidirect |
| 123. C7⋊C16 | #41 | semidirect |
| 170. C4×D7 | SD32 | semidirect |
| 308. C7 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739379 | 2 |
| #11739220 | 2 |
| C7×#2240 | 2 |
| #11729139 | 2 |
| #11729045 | 2 |
| #11726950 | 2 |
| #11726929 | 2 |
| #11726819 | 2 |
| C4×D7×C16 | 2 |
| #33736 | 7 |