Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11729139 | C2 | semidirect |
| 3. #11729114 | C2 | semidirect |
| 6. #11726819 | C2 | semidirect |
| 7. C16×C7⋊C8 | C2 | semidirect |
| 76. C7⋊C16 | SD16 | semidirect |
| 110. C7⋊C8 | SD32 | semidirect |
| 191. C7 | #12505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2240 | 2 |
| #11729139 | 2 |
| #11729114 | 2 |
| #11729045 | 2 |
| #11729028 | 2 |
| #11726819 | 2 |
| C16×C7⋊C8 | 2 |
| #12505 | 7 |